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A new type of CEV model: properties, comparison, and application to portfolio optimization Stoch. Models (IF 0.7) Pub Date : 2024-03-16 Marcos Escobar Anel, Wei Li Fan
This article proposes and studies a new type of constant elasticity of volatility (CEV) model, titled LVO-CEV, where the name indicates that the excess return is linear in the volatility. The model...
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The consistency of the estimators in semiparametric regression model based on m-asymptotic negatively associated errors Stoch. Models (IF 0.7) Pub Date : 2024-03-16 Jiayi Feng, Aiting Shen, Dantong Wang, Xuejun Wang
In this article, we analyze the strong consistency and r-th (r > 1) mean consistency for the estimators βu, n and gu, n of β and g, respectively, based on m-asymptotic negatively associated errors....
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On cover times of Markov chains Stoch. Models (IF 0.7) Pub Date : 2024-03-12 Bruno Sericola
We consider the cover time of a discrete-time homogenous Markov chain, which is the time needed by the Markov chain to visit all its states. We analyze both the distribution and the moments of the ...
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Asymptotic normality for the weighted estimators in heteroscedastic partially linear regression model under dependent errors Stoch. Models (IF 0.7) Pub Date : 2024-03-12 Sallieu Kabay Samura, Xuejun Wang, Yi Wu, Fei Zhang
In this article, we investigate the estimators for the heteroscadastic partially linear regression model under dependent errors defined by yi=xiβ+g(ti)+εi (1≤i≤n), where εi = σiei, σi2=f(ui), the d...
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Clique and cycle frequencies in a sparse random graph model with overlapping communities Stoch. Models (IF 0.7) Pub Date : 2024-03-08 Tommi Gröhn, Joona Karjalainen, Lasse Leskelä
A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes...
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Asymptotic analysis of the sojourn time of a batch in a M[X]/M/1 processor sharing queue Stoch. Models (IF 0.7) Pub Date : 2024-03-05 Fabrice Guillemin, Alain Simonian, Ridha Nasri, Veronica Quintuna Rodriguez
In this article, we exploit recent results for the Laplace transform of the sojourn time Ω of an entire batch in the M[X]/M/1 processor sharing queue in order to derive the asymptotic behavior of t...
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Increasing Gambler’s Ruin duration and Brownian motion exit times Stoch. Models (IF 0.7) Pub Date : 2024-03-01 Erol A. Peköz, Rhonda Righter
In Gambler’s Ruin when both players start with the same amount of money, we show the playing time stochastically increases when the games are made more fair. We give two different arguments for thi...
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Optimal dividend and proportional reinsurance strategy for the risk model with common shock dependence Stoch. Models (IF 0.7) Pub Date : 2024-03-01 Bo Yang, Ruili Song, Dingjun Yao, Gongpin Cheng
This article focuses on the classic optimal dividend and reinsurance problems. Different from the existing literature, it assumes that the insurance company has two lines of business with a common ...
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Numerical approximation of a hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay Stoch. Models (IF 0.7) Pub Date : 2024-02-05 Emmanuel Coffie
While the original Ait-Sahalia interest rate model has been found to be of considerable use for describing the time-series evolution of interest rates, it may not possess adequate specifications to...
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Geometrical interpretation of the population entropy maximum Stoch. Models (IF 0.7) Pub Date : 2024-02-02 Igor Lazov, Petar Lazov
We consider a population of finite size M, where the current number N of entities, N∈{0,1,2,…,M}, determines its states. We geometrically analyze the amounts of information iN and iM−N, carried by ...
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Some convergence properties for arrays of rowwise asymptotically almost negatively associated random variables under sub-linear expectations Stoch. Models (IF 0.7) Pub Date : 2023-12-18 Miaomiao Wang, Shunping Zheng, Xuejun Wang
In this article, under some suitable conditions, we study the Lq convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short)...
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Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance Stoch. Models (IF 0.7) Pub Date : 2023-11-20 Pavel Ievlev
This article investigates the Parisian ruin probability for a class of Gaussian processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptoti...
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Nadaraya-Watson estimators for stochastic differential equations driven by fractional Brownian motion Stoch. Models (IF 0.7) Pub Date : 2023-11-16 Yuecai Han, Dingwen Zhang
In this article, we investigate the nonparametric Nadaraya-Watson estimator for the drift function of stochastic differential equations driven by fractional Brownian motion of the Hurst parameter H...
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A queueing model with ON/OFF sources: approximation and stationarity Stoch. Models (IF 0.7) Pub Date : 2023-10-26 Hongshuai Dai, Yanhua Wu
Fractional Brownian motion approximation of queueing networks has been studied extensively. In the existing results related to this topic, the Hurst parameter of multidimensional fractional Brownia...
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Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement Stoch. Models (IF 0.7) Pub Date : 2023-10-17 Meghdad Mirebrahimi
The Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sur...
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On age composition of dynamic heterogeneous populations Stoch. Models (IF 0.7) Pub Date : 2023-10-19 Ji Hwan Cha, Maxim Finkelstein
Populations of items continuously manufactured and incepted into operation are characterized by the corresponding distribution of a random age at each instant of chronological time. In this study, ...
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Complete f-moment convergence for a class of random variables with related statistical applications Stoch. Models (IF 0.7) Pub Date : 2023-10-11 Liangxue Li, Xuejun Wang, Chen Yi
In this article, we establish the complete f-moment convergence for a class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition with a mean domin...
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The longest edge of the one-dimensional soft random geometric graph with boundaries Stoch. Models (IF 0.7) Pub Date : 2023-09-22 Arnaud Rousselle, Ercan Sönmez
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the ...
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Moments based matrix representation of Markov and rational arrival processes with reduced rank marginal Stoch. Models (IF 0.7) Pub Date : 2023-09-08 András Mészáros, Miklós Telek
Abstract The moments based matrix representation of Markovian and rational arrival processes (MAP/RAPs) with full rank marginal (FRM) is provided in Telek and Horváth[ 14 Telek, M.; Horváth, G. A minimal representation of Markov arrival processes and a moments matching method. Perform. Eval. 2007, 64, 1153–1168. DOI: 10.1016/j.peva.2007.06.001.[Crossref], [Web of Science ®] , [Google Scholar]]. MAP/RAPs
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Mean-field fluctuations at diffusion scale in threshold-based randomized routing for processor sharing systems and applications Stoch. Models (IF 0.7) Pub Date : 2023-09-04 Samira Ghanbarian, Ravi R. Mazumdar
Abstract In this article, we study the fluctuations of the empirical occupation measures of servers around their mean-field limit in a large system of heterogeneous processor sharing servers. It is assumed that there are M different servers grouped by their speeds and that the total number of servers is N. In particular, we study the sensitivity of the fluctuations to arrival rate parameters at the
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Moderate deviations for stochastic Cahn-Hilliard equations with a random dynamical boundary driven by Poisson random measures Stoch. Models (IF 0.7) Pub Date : 2023-09-08 Ying Wang, Guanggan Chen, Pin Wang
Abstract This work concerns a stochastic Cahn-Hilliard equation with a random dynamical boundary condition driven by Poisson random measures. Due to the disturbance of pure jump Lévy noise both in the domain and on its boundary, we drive the tightness of deviation processes by employing the stochastic control argument and the splitting method. With the help of the weak convergence approach, we establish
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Quenched weighted moments for a branching process with immigration in a random environment Stoch. Models (IF 0.7) Pub Date : 2023-08-10 Xulan Huang
Abstract For a supercritical branching process, (Zn)n≥0(Zn)n≥0 with immigration (Yn)n≥0(Yn)n≥0 in an independent and identically distributed random environment ξ=(ξn)n≥0ξ=(ξn)n≥0 . Let W be the limit of the submartingale Wn=Zn/Πn,n≥0 , where (Πn)n≥0 is the usually used normalization sequence. The necessary and sufficient condition for the existence of quenched weighted moments of W of the form Eξ[Wαl(W)]
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A stochastic log-logistic diffusion process: Statistical computational aspects and application to real data Stoch. Models (IF 0.7) Pub Date : 2023-08-09 Abdenbi El Azri, Nafidi Ahmed
Abstract This article introduces a new stochastic diffusion process based on the theory of diffusion processes whose mean function is proportional to the log-logistic growth curve. The main characteristics of the process are analyzed, including the transition probability density function, the mean functions and in particular, the auto-correlation function between two times of the process. The parameters
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Gambler’s ruin with random stopping Stoch. Models (IF 0.7) Pub Date : 2023-08-03 Gregory J. Morrow
Abstract Let {Xj,j≥0}{Xj,j≥0} denote a Markov process on [−N−1,N+1]∪{c}[−N−1,N+1]∪{c} . Suppose P(Xj+1=m+1|Xj=m)=ph,P(Xj+1=m−1|Xj=m)=(1−p)hP(Xj+1=m+1|Xj=m)=ph,P(Xj+1=m−1|Xj=m)=(1−p)h , all j≥1j≥1 and |m|≤N , where p=12+bN and h=1−cN for cN=12a2/N2. Define P(Xj+1=c|Xj=m)=cN,j≥0,|m|≤N. {Xj} terminates at the first j such that Xj∈{−N−1,N+1,c}. Let L=max{j≥0:Xj=0}. On Ω°={Xj terminates at c}, denote by
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Optimizing Erlangization-based approximations for finite discrete distributions and discrete phase-type distributions Stoch. Models (IF 0.7) Pub Date : 2023-07-07 Haoran Wu, Qi-Ming He
Abstract In He et al.[8 Buchholz, P.; Kriege, J.; Felko, I. Input Modeling with Phase-type Distributions and Markov Models: Theory and Applications; Berlin, Germany: Springer, 2014.[Crossref] , [Google Scholar]], continuous phase-type (PH) distributions are constructed to approximate finite discrete probability distributions and discrete PH-distributions. The approximations are based on Erlangization
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Robust optimal asset-liability management under square-root factor processes and model ambiguity: a BSDE approach Stoch. Models (IF 0.7) Pub Date : 2023-07-07 Yumo Zhang
Abstract This article studies robust optimal asset-liability management problems for an ambiguity-averse manager in a possibly non-Markovian environment with stochastic investment opportunities. The manager has access to one risk-free asset and one risky asset in a financial market. The market price of risk relies on a stochastic factor process satisfying an affine-form, square-root, Markovian model
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A general result on complete f-moment convergence with its application to nonparametric regression models Stoch. Models (IF 0.7) Pub Date : 2023-06-10 Shunping Zheng, Fei Zhang, Chunhua Wang, Xuejun Wang
In this paper, the complete f-moment convergence for weighted sums of sequences of extended negatively dependent random variables is investigated. As a result, we not only extend and generalize som...
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On the Gaussian Volterra processes with power-type kernels Stoch. Models (IF 0.7) Pub Date : 2023-05-19 Mohamed El Omari
We consider the Gaussian Volterra process Xθ={Xθ(t),t∈[0,T]}, θ=(α,β,γ) introduced in Mishura and Shklyar [Theory and Applications 2022a, 431–452] We specify the parameters θ for which Xθ is non Ma...
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Stochastic epidemic spreading: not all super-spreading processes are born equal, neither all lockdown strategies Stoch. Models (IF 0.7) Pub Date : 2023-05-12 Jhonatan Tavori, Hanoch Levy
We consider viral spreading processes, such as pandemics, in finite networks. For such processes, we propose and analyze a new model which combines two stochastic functions in the spreading intensi...
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Asymptotics for a diffusion-perturbed risk model with dependence structures, constant interest force, and a random number of delayed claims Stoch. Models (IF 0.7) Pub Date : 2023-05-09 Xijun Liu, Qingwu Gao, Zimai Dong
During extreme events such as natural or man-made disasters, it is likely that after immediate claims directly caused by the events, there are other delayed claims occurring in a certain period of ...
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Asymptotic efficiency in autoregressive processes driven by stationary Gaussian noise Stoch. Models (IF 0.7) Pub Date : 2023-05-02 Marius Soltane
In this study, almost sure asymptotic properties of the maximum likelihood estimator in an autoregressive process driven by stationary Gaussian noise are obtained. Precisely, we show that the maxim...
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Joint discrete and continuous matrix distribution modeling Stoch. Models (IF 0.7) Pub Date : 2023-03-28 Martin Bladt, Clara Brimnes Gardner
In this paper, we introduce a bivariate distribution on R+×N arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, res...
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Connection intervals in multi-scale infrastructure-augmented dynamic networks Stoch. Models (IF 0.7) Pub Date : 2023-03-06 Christian Hirsch, Benedikt Jahnel, Elie Cali
We consider a hybrid spatial communication system in which mobile nodes can connect to static sinks in a bounded number of intermediate relaying hops. We describe the distribution of the connection...
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The stochastic Leibniz formula for Volterra integrals under enlarged filtrations Stoch. Models (IF 0.7) Pub Date : 2023-02-28 Markus Hess
In this paper, we derive stochastic Leibniz formulas for Volterra integrals under enlarged filtrations. We investigate both pure-jump and Brownian Volterra processes under diverse initially enlarge...
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Correction Stoch. Models (IF 0.7) Pub Date : 2023-02-24
Published in Stochastic Models (Ahead of Print, 2023)
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Sequences of random matrices modulated by a discrete-time Markov chain* Stoch. Models (IF 0.7) Pub Date : 2023-02-15 George Yin, Huy Nguyen
In this work, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space. Assuming that the state space of the Markov chain is l...
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A q-binomial extension of the CRR asset pricing model Stoch. Models (IF 0.7) Pub Date : 2023-02-08 Jean-Christophe Breton, Youssef El-Khatib, Jun Fan, Nicolas Privault
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider ...
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A new mixed δ-shock model and associated reliability properties Stoch. Models (IF 0.7) Pub Date : 2023-01-23 Rasool Roozegar, Marjan Entezari, N. Balakrishnan, Saraleean Nadarajah
Abstract In reliability literature, shock models and multi-state systems have both been discussed extensively. Shock models have attracted a great deal of attention due to their important role in engineering systems. In the δ-shock model, a system fails if the interval time between two successive shocks is less than a pre-fixed threshold δ. In this study, a new version of mixed δ-shock models is defined
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Constrained mean-variance portfolio optimization for jump-diffusion process under partial information Stoch. Models (IF 0.7) Pub Date : 2023-01-23 Caibin Zhang, Zhibin Liang
This article studies a mean-variance portfolio selection problem for a jump-diffusion model, where the drift process is modulated by a continuous unobservable Markov chain. Since there is a constra...
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Estimation of stress-strength reliability for multicomponent system with a generalized inverted exponential distribution Stoch. Models (IF 0.7) Pub Date : 2023-01-12 Liang Wang, Shuo-Jye Wu, Sanku Dey, Yogesh Mani Tripathi, Song Mao
Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) wi...
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Complete f-moment convergence for arrays of rowwise m-negatively associated random variables and its statistical applications Stoch. Models (IF 0.7) Pub Date : 2023-01-09 Miaomiao Wang, Min Wang, Xuejun Wang, Fei Zhang
Abstract In this paper, we study the complete f-moment convergence for arrays of rowwise m-negatively associated random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As an application of the main results, we present the complete consistency for the estimator in a semiparametric regression model based on m-negatively associated
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The estimation in Pólya–Eggenberger urn model with a delay Stoch. Models (IF 0.7) Pub Date : 2022-12-29 Babak Jamshidi, Parisa Torkaman
Abstract In this article, we introduce a new model derived from Pólya–Eggenberger urn model. This model is defined by considering a delay in collecting information. The mathematical formulation of this model is done through four parameters; the number of balls in the first structure (N0), the number of white balls in the first structure (W0), the number of rewarded balls of the color of the ball withdrawn
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A stochastic delayed SIS epidemic model with Holling type II incidence rate Stoch. Models (IF 0.7) Pub Date : 2022-12-22 Wenxu Dong, Jianjun Zhou, Biteng Xu
Abstract In this article, a stochastic SIS epidemic model with constant time delay and Holling type II incidence rate is investigated. We firstly show the existence, uniqueness, and moment boundedness of the global positive solution. Then we extend the initial value space to a complete nonnegative continuous function space and obtain the existence of invariant measures for this system. Furthermore
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Maintenance effort expense modeling based on cyclic Wiener processes of two types for edge OSS computing Stoch. Models (IF 0.7) Pub Date : 2022-12-07 Yoshinobu Tamura, Shigeru Yamada
Abstract The appropriate control of maintenance effort in the edge computing based on open-source software (OSS) relates to stable and reliable operation, because the fault detection phenomenon depends on the effort expenditure. Actually, several software reliability growth models with testing-effort have been proposed in the past. In this paper, we propose cyclic Wiener process models to consider
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Periodic review inventory models with multiclass demands and fixed order costs Stoch. Models (IF 0.7) Pub Date : 2022-11-21 Vidyadhar G. Kulkarni, Li Xiao, Hanqin Zhang
Abstract We consider a periodic review inventory system with multiclass demands and fixed setup cost. Demand arrivals of each class are assumed to be a Poisson process, and a lost-sales setting is adopted. The demand classes are classified by the cost of their unsatisfied demands. We consider two cases: the leftover inventory at the end of a restocking interval is entirely discarded or entirely carried
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Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources Stoch. Models (IF 0.7) Pub Date : 2022-11-18 Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
Abstract This work contributes to the theory of Hawkes processes. We introduce and study a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass – the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for
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Asset-liability management with state-dependent utility in the regime-switching market Stoch. Models (IF 0.7) Pub Date : 2022-11-11 Xiufang Li, Dongxu Zhao, Xiaowei Chen
Abstract This paper considers a state-dependent optimal asset-liability management problem in continuous-time settings. The investor maximizes the expected state-dependent utility of the terminal asset-liability ratio in a regime-switching market to better describe insurance companies’ needs for asset-liability matching and regulation with background risk. We apply the stochastic dynamic programming
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Preface of the special issue on Branching Processes and Applications (IWBPA2021) Stoch. Models (IF 0.7) Pub Date : 2022-11-07 M. González, M. Molina, I. del Puerto
Published in Stochastic Models (Vol. 39, No. 1, 2023)
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Singular perturbation for a two-class processor-sharing queue with impatience Stoch. Models (IF 0.7) Pub Date : 2022-10-25 R. Nasri, F. Simatos, A. Simonian
Abstract A two-class Processor-Sharing queue with one impatient class is studied. Local exponential decay rates for its stationary distribution (N(∞),M(∞))(N(∞),M(∞)) are established in the heavy traffic regime where the arrival rate of impatient customers grows proportionally to a large factor A. This regime is characterized by two time-scales, so that no general Large Deviations result is applicable
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Complete q-th moment convergence for the maximum of partial sums of m-negatively associated random variables and its application to the EV regression model* Stoch. Models (IF 0.7) Pub Date : 2022-09-16 Fen Jiang, Miaomiao Wang, Xuejun Wang
Abstract In this article, we prove the complete q-th moment convergence for the maximum of partial sums of m-negatively associated random variables {Xn,n≥1} under some general conditions. The results obtained in this article are extensions of previous studies for m-negatively associated random variables. In addition, we investigate the strong consistency of the least squares estimator in the simple
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Residue expansions and saddlepoint approximations in stochastic models using the analytic continuation of generating functions Stoch. Models (IF 0.7) Pub Date : 2022-09-15 Ronald W. Butler
Abstract Asymptotic residue expansions are proposed for inverting probability generating functions (PGFs) and approximating their associated mass and survival functions. The expansions are useful in the wide range of stochastic model applications in which a PGF admits poles in its analytic continuation. The error of such an expansion is a contour integral in the analytic continuation and saddlepoint
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Sensitivity analysis for a Markov regenerative software rejuvenation model Stoch. Models (IF 0.7) Pub Date : 2022-09-10 Junjun Zheng, Hiroyuki Okamura, Tadashi Dohi
Abstract This article considers the parametric sensitivity of a software rejuvenation model for transaction systems whose system behavior is described by a quasi-birth-and-death (QBD) process with Markovian arrivals, and the software rejuvenation model is represented by a Markov regenerative process (MRGP). The stationary analysis of the MRGP model is based on the embedding Markov chain (EMC) approach
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MTTF and availability of semi-Markov missions with non-identical generally distributed component lifetimes Stoch. Models (IF 0.7) Pub Date : 2022-08-27 Bora Çekyay, Süleyman Özekici
Abstract We analyze mean time to failure and availability of systems that perform semi-Markov missions. The mission process is the minimal semi-Markov process associated with a Markov renewal process. Therefore, the successive phases of the mission follow a Markov chain, and the phase durations are generally distributed. The lifetimes of the non-identical components in the system are assumed to be
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Some results on stochastic comparisons of two finite mixture models with general components Stoch. Models (IF 0.7) Pub Date : 2022-08-22 Suchandan Kayal, Raju Bhakta, N. Balakrishnan
Abstract Finite mixture (FM) models have found key applications in many fields. Recently, some discussions have been made on comparing finite mixture models. In this paper, we discuss stochastic comparison of two FM models with respect to usual stochastic order when the mixture components have a general family of distributions. This problem has been studied when there is heterogeneity in one parameter
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Hidden equations of risk critical thresholds Stoch. Models (IF 0.7) Pub Date : 2022-08-19 Vladimir V. Ejov, Jerzy A. Filar, Zhihao Qiao
Abstract We consider the problem of parametric sensitivity of a particular characterization of risk, with respect to a threshold parameter δ. Such threshold risk is modeled as the probability of a δ−perturbed function of a random variable falling below 0. We demonstrate that for polynomial and rational functions of that random variable there exist at most finitely many risk critical points. The latter
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Diffusion approximations for periodically arriving expert opinions in a financial market with Gaussian drift Stoch. Models (IF 0.7) Pub Date : 2022-08-15 Jörn Sass, Dorothee Westphal, Ralf Wunderlich
Abstract In this paper we study a financial market in which stock returns depend on an unobservable Gaussian drift process. Investors obtain information on that drift from return observations and discrete-time expert opinions as an external source of information. Estimates of the hidden drift process are based on filtering techniques. Our focus is the case of high-frequency experts periodically providing
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Economic shipping policies for assuring safety integrity level of E/E/PE safety-related software Stoch. Models (IF 0.7) Pub Date : 2022-08-09 Shinji Inoue, Shigeru Yamada, Takaji Fujiwara
Abstract Electrical/electronic/programmable electronic (E/E/PE) safety-related systems are widely applied in several industrial fields due to noticeable technical growth of information processing technologies. In the design and development for the E/E/PE safety-related software, safety assessment is required by following IEC 61508, which is the international basic standard for the E/E/PE safety-related
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Stochastic models of stem cells and their descendants under different criticality assumptions Stoch. Models (IF 0.7) Pub Date : 2022-07-06 Nam H. Nguyen, Marek Kimmel
Abstract We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized by the mutation rate of the original cells and the survival probability of the altered cells’ progeny. For each system, we derive a closed-form expression
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Continuous scaled phase-type distributions Stoch. Models (IF 0.7) Pub Date : 2022-07-05 Hansjörg Albrecher, Martin Bladt, Mogens Bladt, Jorge Yslas
Abstract Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective statistical inference is derived and implemented using real-world datasets. In contrast to discrete scaling studied in earlier literature, in the present
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Diffusion approximation of controlled branching processes using limit theorems for random step processes Stoch. Models (IF 0.7) Pub Date : 2022-06-24 Miguel González, Pedro Martín-Chávez, Inés M. del Puerto
Abstract A controlled branching process (CBP) is a modification of the standard Bienaymé–Galton–Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random number of initial individuals. The main aim of this article is to provide a Feller diffusion approximation for critical CBPs. A similar result by considering