Pathwise Ito calculus for rough paths and rough PDEs with path dependent coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Keller, Christian¹  Zhang, Jianfeng² 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

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

关键词: Rough path;    Functional Ito calculus;    Path derivatives;    Ito-Ventzell formula;    Rough differential equations;    Rough PDEs;    Stochastic PDEs;    Characteristics;   

DOI  :  10.1016/j.spa.2015.09.018

来源: Elsevier

【 摘 要 】

This paper introduces path derivatives, in the spirit of Dupire's functional Ito calculus, for controlled rough paths in rough path theory with possibly non-geometric rough paths. We next study rough PDEs with coefficients depending on the rough path itself, which corresponds to stochastic PDEs with random coefficients. Such coefficients are less regular in the time variable, which is not covered in the existing literature. The results are useful for studying viscosity solutions of stochastic PDEs. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free