Stochastic calculus for tempered fractional Brownian motion and stability for SDEs driven by TFBM

被引：2
|
作者：
Zhang, Lijuan [1 ]
Wang, Yejuan [1 ]
Hu, Yaozhong [2 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2024年 / 42卷 / 01期
基金：
中国国家自然科学基金; 加拿大自然科学与工程研究理事会;
关键词：
Tempered fractional Brownian motion; Stochastic integral; Malliavin calculus; Wick product; Ito formula; stochastic differential equation; general decay; stochastic stability; EXPONENTIAL STABILITY; EVOLUTION-EQUATIONS;
D O I：
10.1080/07362994.2023.2192267
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The objective of this article is to introduce and study Ito type stochastic integrals with respect to tempered fractional Brownian motion (TFBM) of Hurst index H ? (1/2,1) and tempering parameter ? > 0, by using the Wick product. The main tools are fractional calculus and Malliavin calculus. The Ito formula for this stochastic integral is established for the Ito type processes driven by TFBM. Based on this new Ito formula, we analyze the stability of stochastic differential equations driven by TFBM in the sense of p-th moment. A numerical example is given to illustrate our stability results.
引用
收藏
页码：64 / 97
页数：34
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