Stochastic calculus with respect to Gaussian processes

• 成果类型: Article
• 署名作者: Alòs, E; Mazet, O; Nualart, D
• 署名单位: Autonomous University of Barcelona; University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1008956692
• 发表日期: 2001
• 页码: 766-801
• 关键词: formula

摘要

In this paper we develop a stochastic calculus with respect to a Gaussian process of the form B-t = integral (t)(0) K(t, s) dW(s), where W is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums. The particular case of the fractional Brownian motion is discussed.