非线性乘性混合噪声驱动下spde的存在唯一性

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-02-25 DOI:10.1016/j.spa.2025.104612

Shiduo Qu, Hongjun Gao

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引用次数: 0

摘要

研究了一类由标准布朗运动和分数布朗运动驱动的随机偏微分方程（SPDEs），其Hurst参数为H>；1/2。我们在几乎肯定的意义上建立了这些spde解的存在唯一性。进一步证明了解的矩是有限的。此外，我们还探讨了分数阶导数定义的积分与缝纫引理定义的积分之间的等价性。

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Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise

This paper investigates a class of stochastic partial differential equations (SPDEs) driven by standard Brownian motion and fractional Brownian motion with Hurst parameter

H > 1 / 2

. We establish the existence and uniqueness of solutions for these SPDEs in sense of almost surely. We further prove that the moments of the solutions are finite. Moreover, we explore the equivalence between the integral defined by fractional derivatives and that defined by sewing lemma.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.