Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs
Analysis of PDEs
2016-04-11 v1
Abstract
In this paper we propose a new type of viscosity solutions for fully nonlinear path dependent PDEs. By restricting to certain pseudo Markovian structure, we remove the uniform non- degeneracy condition imposed in our earlier works [9, 10]. We establish the comparison principle under natural and mild conditions. Moreover, as applications we apply our results to two important classes of PPDEs: the stochastic HJB equations and the path dependent Isaacs equations, induced from the stochastic optimization with random coefficients and the path dependent zero sum game problem, respectively.
Keywords
Cite
@article{arxiv.1604.02239,
title = {Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs},
author = {Ibrahim Ekren and Jianfeng Zhang},
journal= {arXiv preprint arXiv:1604.02239},
year = {2016}
}
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42 pages