Pathwise uniqueness for singular stochastic Volterra equations with Hölder coefficients

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-08-14 DOI:10.1007/s40072-024-00335-y

David J. Prömel, David Scheffels

引用次数: 0

Abstract

Pathwise uniqueness is established for a class of one-dimensional stochastic Volterra equations driven by Brownian motion with singular kernels and Hölder continuous diffusion coefficients. Consequently, the existence of unique strong solutions is obtained for this class of stochastic Volterra equations.

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具有赫尔德系数的奇异随机 Volterra方程的路径唯一性

对于一类由具有奇异核和霍尔德连续扩散系数的布朗运动驱动的一维随机伏特拉方程，建立了路径唯一性。因此，该类随机 Volterra 方程存在唯一的强解。

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

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.