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

Sixian Jin | Zendy; Henry Schellhorn | Zendy

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

Author(s) -

Sixian Jin,

Henry Schellhorn

Publication year - 2017

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2017/2876961

Subject(s) - mathematics , semigroup , parabolic partial differential equation , partial differential equation , path (computing) , mathematical analysis , order (exchange) , derivative (finance) , malliavin calculus , analytic semigroup , generator (circuit theory) , heat equation , path dependent , first order partial differential equation , elliptic partial differential equation , partial derivative , representation (politics) , stochastic partial differential equation , power (physics) , physics , finance , quantum mechanics , politics , computer science , political science , law , programming language , financial economics , economics

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

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