Pathwise Taylor expansions for random fields on multiple dimensional paths

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Buckdahn, Rainer^1,2  Ma, Jin³  Zhang, Jianfeng³ 

[1] Univ Bretagne Occidentale, Dept Math, F-29285 Brest, France

[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[3] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

关键词: Path derivatives;    Pathwise Taylor expansion;    Functional Ito formula;    Ito-Wentzell formula;    Stochastic partial differential equations;   

DOI  :  10.1016/j.spa.2015.02.004

来源: Elsevier

【 摘 要 】

In this paper we establish the pathwise Taylor expansions for random fields that are regular in terms of Dupire's path-derivatives [6]. Using the language of pathwise calculus, we carry out the Taylor expansion naturally to any order and for any dimension, which extends the result of Buckdahn et al. (2011). More importantly, the expansion can be both forward and backward, and the remainder is estimated in a pathwise manner. This result will be the main building block for our new notion of viscosity solution to forward path-dependent PDEs corresponding to (forward) stochastic PDEs in our accompanying paper Buckdahn et al. [4]. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free