Solving stochastic equations with unbounded nonlinear perturbations

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2023-09-13 DOI:10.1080/17442508.2023.2258248

Mohamed Fkirine, Said Hadd

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引用次数: 0

Abstract

AbstractThis paper is interested in semilinear stochastic equations having unbounded nonlinear perturbations in the deterministic part and/or in the random part. Moreover, the linear part of these equations is governed by a not necessarily analytic semigroup. The main difficulty with these equations is how to define the concept of mild solutions due to the chosen type of unbounded perturbations. To overcome this problem, we first proved a regularity property of the stochastic convolution with respect to the domain of ‘admissible’ unbounded linear operators (not necessarily closed or closable). This is done using Yosida extensions of such unbounded linear operators. After proving the well-posedness of these equations, we also establish the Feller property for the corresponding transition semigroups. Several examples like heat equations and Schrödinger equations with nonlocal perturbations terms are given. Finally, we give an application to a general class of semilinear neutral stochastic equations.Keywords: Semilinear stochastic equationsunbounded nonlinear perturbationHilbert spacesemigroupequations with delays Disclosure statementNo potential conflict of interest was reported by the author(s).

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求解具有无界非线性扰动的随机方程

摘要本文研究了在确定性部分和(或)随机部分具有无界非线性扰动的半线性随机方程。此外，这些方程的线性部分不一定由解析半群控制。这些方程的主要困难是如何定义由于所选择的无界扰动类型而产生的温和解的概念。为了克服这个问题，我们首先证明了随机卷积在“可容许的”无界线性算子(不一定是闭的或可闭的)域中的正则性。这是使用Yosida扩展的无界线性算子完成的。在证明了这些方程的适定性之后，我们还建立了相应转移半群的Feller性质。给出了一些具有非局部扰动项的热方程和Schrödinger方程的例子。最后，我们给出了一类一般的半线性中立型随机方程的一个应用。关键词:半线性随机方程;有界非线性摄动;希尔伯特空间;

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-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.