Large time behaviour of semilinear stochastic partial differential equations perturbed by a mixture of Brownian and fractional Brownian motions

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE Finance and Stochastics Pub Date : 2023-01-23 DOI:10.1080/17442508.2023.2167518

M. Dozzi, E. T. Kolkovska, J. López-Mimbela, Rim Touibi

引用次数: 2

Abstract

We study the trajectorywise blowup behaviour of a semilinear partial differential equation that is driven by a mixture of multiplicative Brownian and fractional Brownian motion, modelling different types of random perturbations. The linear operator is supposed to have an eigenfunction of constant sign, and we show its influence, as well as the influence of its eigenvalue and of the other parameters of the equation, on the occurrence of a blowup in finite time of the solution. We give estimates for the probability of finite time blowup and of blowup before a given fixed time. Essential tools are the mild and weak form of an associated random partial differential equation.

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由布朗运动和分数布朗运动混合扰动的半线性随机偏微分方程的大时间行为

我们研究了由乘法布朗运动和分数布朗运动混合驱动的半线性偏微分方程的轨迹爆炸行为，模拟了不同类型的随机扰动。假设线性算子具有一个常符号的特征函数，并给出了它的影响，以及它的特征值和方程的其他参数对解在有限时间内出现爆破的影响。给出了有限时间爆炸和在给定固定时间前爆炸的概率估计。基本工具是相关随机偏微分方程的弱和弱形式。

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

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.

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