Approximation of stochastic differential equations driven by subfractional Brownian motion at discrete time observation. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Shen, Guangjun; Tang, Zheng; Wang, Jun
• Is Part Of: Communications in statistics. Volume 52:Issue 1(2023)
• Page Start: 1
• Page End: 18
• Publication Date: 2023-01-02
• Subjects: Subfractional Brownian motion -- Gaussian processes -- discrete time approximation; 60F17 -- 60G15 -- 60G18 -- 60G22; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1901924
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we consider discrete time approximations for stochastic differential equations with the form: M0001 X t = X 0 + ∫ 0 t f ( X s ) d h s + ∫ 0 t g ( X s ) d Y s H, t > 0, where h : R + → R is a continuous function with locally bounded variation, f, g : R → R are measurable functions, and the integral with respect to Y t H = ∫ 0 t σ s d S s H is the pathwise Riemann-Stieltjes integral, S H is a subfractional Brownian motion with H ∈ ( 1 2, 1 ), σ is a deterministic (possibly discontinuous) function.