Pathwise Taylor expansions for random fields on multiple dimensional paths

Stochastic Processes and their Applications - Tập 125 - Trang 2820-2855 - 2015
Rainer Buckdahn1,2, Jin Ma3, Jianfeng Zhang3
1Département de Mathématiques, Université de Bretagne-Occidentale, F-29285 Brest Cedex, France
2School of Mathematics, Shandong University, Jinan 250100, PR China
3Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Tài liệu tham khảo

Bichteler, 1981, Stochastic integration and Lp-theory of semi-martingales, Ann. Probab., 9, 48, 10.1214/aop/1176994509 Buckdahn, 2011, Pathwise Taylor expansions for Itô random fields, Math. Control Relat. Fields, 1, 437, 10.3934/mcrf.2011.1.437 Buckdahn, 2002, Pathwise stochastic Taylor expansions and stochastic viscosity solutions for fully nonlinear stochastic PDEs, Ann. Probab., 30, 1131, 10.1214/aop/1029867123 R. Buckdahn, J. Ma, J. Zhang, Pathwise viscosity solutions for stochastic PDEs and forward path dependent PDEs, Preprint. arXiv:1501.06978. Cont, 2013, Functional Itô calculus and stochastic integral representation of martingales, Ann. Probab., 41, 109, 10.1214/11-AOP721 B. Dupire, Functional Itô calculus, papers.ssrn.com. Ekren, 2015, Viscosity solutions of fully nonlinear parabolic path dependent PDEs: part I, Ann. Probab. Friz, 2014 Friz, 2010 Gilbarg, 1998 Karandikar, 1995, On pathwise stochastic integration, Stochastic Process. Appl., 57, 11, 10.1016/0304-4149(95)00002-O Kloeden, 1992 Krylov, 1999, An analytic approach to SPDEs, vol. 64, 185 C. Litterer, H. Oberhauser, A Chen-Fliess approximation for diffusion functionals, Preprint. arXiv:1110.2481. Lyons, 2007, vol. 1908 Ma, 1999, On linear backward stochastic partial differential equations, Probab. Theory Related Fields, 113, 135, 10.1007/s004400050205 Rozovskii, 1990