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July 2016 An infinite-dimensional approach to path-dependent Kolmogorov equations
Franco Flandoli, Giovanni Zanco
Ann. Probab. 44(4): 2643-2693 (July 2016). DOI: 10.1214/15-AOP1031

Abstract

In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated and solved both in the space of $L^{p}$ paths and in the space of continuous paths using the associated stochastic differential equation, thus establishing a relation between path-dependent SDEs and PDEs in analogy with the classical case. Finally, it is shown how to establish a connection between such Kolmogorov equation and the analogue finite-dimensional equation that can be formulated in terms of the path-dependent derivatives recently introduced by Dupire, Cont and Fournié.

Citation

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Franco Flandoli. Giovanni Zanco. "An infinite-dimensional approach to path-dependent Kolmogorov equations." Ann. Probab. 44 (4) 2643 - 2693, July 2016. https://doi.org/10.1214/15-AOP1031

Information

Received: 1 December 2013; Revised: 1 April 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1356.60101
MathSciNet: MR3531677
Digital Object Identifier: 10.1214/15-AOP1031

Subjects:
Primary: 35C99, 35K99, 60H10, 60H30

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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