Differentiation formula in Stratonovich version for fractional Brownian sheet

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:359

Article

Kim, Yoon Tae²  Jeon, Jong Woo³  Park, Hyun Suk¹ 

[1] POSTECH, Pohang Math Inst, Pohang 790784, South Korea

[2] Hallym Univ, Dept Stat, Chunchon 200702, South Korea

[3] Seoul Natl Univ, Dept Stat, Seoul 151742, South Korea

关键词: Fractional Brownian sheet;    Malliavin derivative;    Stratonovich stochastic integral;    Differentiation formula;   

DOI  :  10.1016/j.jmaa.2009.05.037

来源: Elsevier

【 摘 要 】

We introduce two types of the Stratonovich stochastic integrals for two-parameter processes, and investigate the relationship of these Stratonovich integrals and various types of Skorohod integrals with respect to a fractional Brownian sheet. By using this relationship. we derive a differentiation formula in the Stratonovich sense for fractional Brownian sheet through Ito formula. Also the relationship between the two types of the Stratonovich integrals will be obtained and used to derive a differentiation formula in the Stratonovich sense. In this case. our proof is based on the repeated applications of differentiation formulas in the Stratonovich form for one-parameter Gaussian processes. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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