State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations

On Zero-Sum Stochastic Differential Games with Jump-Diffusion Driven State: A Viscosity Solution Framework

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial differential equations. We start by a quick review of the CrandallIshii notion of viscosity solutions, so as to motivate the relevance of our definition in the path-dependent case. We focus on the wellposedness theory of such equations. In particular, we provide a simple presentatio...

Path integral control and state-dependent feedback.

In this paper we address the problem of computing state-dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parametrized state-dependent feedback controllers. In addition, we show a relation between control and importance sampling: Better control, in terms of control cost, yields more efficient...

Path Integral Methods for Stochastic Differential Equations

Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and...

Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

This paper deals with zero-sum stochastic differential games with long-run average payoffs. Our main objective is to give conditions for existence and characterization of bias and overtaking optimal equilibria. To this end, first we characterize the family of optimal average payoff strategies. Then, within this family, we impose suitable conditions to determine the subfamilies of bias and overt...