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
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
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