Differentiation formula in Stratonovich version for fractional Brownian sheet

被引：3
|
作者：
Kim, Yoon Tae [2 ]
Jeon, Jong Woo [3 ]
Park, Hyun Suk [1 ]
机构：
[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
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 359卷 / 01期
关键词：
Fractional Brownian sheet; Malliavin derivative; Stratonovich stochastic integral; Differentiation formula; ITOS FORMULA; MOTION; RESPECT; INTEGRALS; CALCULUS;
D O I：
10.1016/j.jmaa.2009.05.037
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：106 / 125
页数：20
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