Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2022-08-30 DOI:10.1080/17442508.2022.2114801

Jiaping Wen, P. He, Wujun Lv

引用次数: 0

Abstract

ABSTRACT This paper aims to investigate a fractional neutral stochastic functional differential equation (FNSFDE) with non-Lipschitz coefficients. Under the assumptions, we first establish the continuity of the solution in the fractional order of the equation. Furthermore, an Euler-Maruyama (EM) approximation is constructed and then we obtain the strong convergence of the numerical scheme. Specially, if the non-Lipschitz conditions are replaced with the Lipschitz conditions, we shall get a definite convergence rate, which is related to the fractional order of the equation. Finally, we consider the averaging principle for the fractional neutral stochastic equation, which provides us with an easy way to study the properties of the equation.

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非lipschitz系数分数中立型随机泛函微分方程解的连续性和逼近性

摘要研究一类具有非lipschitz系数的分数中立型随机泛函微分方程(FNSFDE)。在此假设条件下，首先建立了方程分数阶解的连续性。进一步构造了Euler-Maruyama (EM)近似，得到了数值格式的强收敛性。特别地，如果用Lipschitz条件代替非Lipschitz条件，我们将得到一个确定的收敛速率，它与方程的分数阶有关。最后，我们考虑了分数中立型随机方程的平均原理，这为我们研究该方程的性质提供了一种简便的方法。

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.