Existence and Uniqueness of Strong Solutions of Mixed-Type Stochastic Differential Equations Driven by Fractional Brownian Motions with Hurst Exponents $$H>1/4 $$

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-09-19 DOI:10.1134/s0012266124060016

M. M. Vas’kovskii, P. P. Stryuk

引用次数: 0

Abstract

We study the unique solvability of the Cauchy problem for a mixed-type stochastic differential equation driven by the standard Brownian motion and fractional Brownian motions with Hurst exponents $H>1/4$. We prove a theorem on the existence and uniqueness of strong solutions of these stochastic differential equations.

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具有赫斯特指数 $$H>1/4 $$ 的分数布朗运动驱动的混合型随机微分方程强解的存在性和唯一性

摘要我们研究了由标准布朗运动和具有赫斯特指数（H>1/4\）的分数布朗运动驱动的混合型随机微分方程的唯一可解性。我们证明了这些随机微分方程强解的存在性和唯一性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.