Abstract

We prove that the \(p\)th moments, \(p\ge 1 \), of strong solutions of a mixed-type stochastic differential equation driven by a standard Brownian motion and a fractional Brownian motion with Hurst index greater than \(1/2\) are finite provided that the coefficients of the equation, together with all of their partial derivatives of order \(\le 2 \), are continuous and bounded and the \(p \)th moment of the initial condition is finite.

中文翻译：

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由标准和分数布朗运动驱动的混合型随机微分方程解的矩的有限性

摘要

我们证明了由标准布朗运动和分数布朗运动驱动的混合型随机微分方程的强解的第（n）个矩 \（p \ ge 1 \）的强解，其Hurst指数大于\（ 1/2 \）的有限提供的方程的系数，与所有的命令他们的偏导数一起 （\文件2 \）\，是连续的并且限定和 \（p \）个初始条件的时刻是有限。