Abstract

The connections between stochastic differential equations in which continuous and discontinuous random processes serve as sources of randomness and deterministic equations for the probabilistic characteristics of solutions of these stochastic equations are studied. In the study, we use various approaches based on the stochastic change of variables formula (Itô’s formula), on the analysis of local infinitesimal characteristics of the process, and on the theory of semigroups of operators in combination with the generalized Fourier transform. This allows us to obtain direct and inverse integro-differential equations for various probabilistic characteristics.

中文翻译：

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随机问题产生的积分微分方程

摘要

研究了以连续和不连续随机过程为随机源的随机微分方程之间的联系，并研究了这些随机方程解的概率特征的确定性方程。在研究中，我们使用多种方法，这些方法基于变量公式（Itô公式）的随机变化，过程的局部无穷小特征分析以及基于广义傅里叶变换的算子半群理论。这使我们可以获得各种概率特征的正整数和逆整数微分方程。