Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations

Sixian Jin and Henry Schellhorn

International Journal of Stochastic Analysis, 2017, vol. 2017, 1-12

Abstract:

We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:2876961

DOI: 10.1155/2017/2876961

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