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

Sixian Jin & Henry Schellhorn

International Journal of Stochastic Analysis2017https://doi.org/10.1155/2017/2876961article
ABDC B
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0.26

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.

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https://doi.org/https://doi.org/10.1155/2017/2876961

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@article{sixian2017,
  title        = {{Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations}},
  author       = {Sixian Jin & Henry Schellhorn},
  journal      = {International Journal of Stochastic Analysis},
  year         = {2017},
  doi          = {https://doi.org/https://doi.org/10.1155/2017/2876961},
}

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

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0.26

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.00 × 0.4 = 0.00
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