Open Access
Translator Disclaimer
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


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.


Download Citation

Franco Flandoli. Giovanni Zanco. "An infinite-dimensional approach to path-dependent Kolmogorov equations." Ann. Probab. 44 (4) 2643 - 2693, July 2016.


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

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

Keywords: delay equations , Kolmogorov equations , path-dependent PDEs , Path-dependent SDEs , stochastic calculus in Banach spaces

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 4 • July 2016
Back to Top