The existence of admissible strategies γ(⋅,⋅) minimizing a function E\int_0^1c(t,x,γ(t,x))dt is
studied, with x=x(⋅,ω) a continuous stochastic process, and admissible strategies defined as …

We give an approach to optimal control of systems described by stochastic functional-
differential equations of Itô's type: dx(t)=f(t,x,u(t,x))dt+dw(t)), 0\leqqt\leqq1, with a cost …

This is a natural generalization of unconditional extremum problems and is encountered in
practical applications. However, the literature has dealt only with the case of a conditional …

The optimal control problem where the state is governed by an Itô stochastic differential
equation (possibly just an ordinary differential equation) is formulated in martingale terms …

Mathematical theory of discrete time decision processes, also known as stochastic control, is
based on two major ideas: backward induction and conditioning. It has a large number of …

In this paper a sufficient condition is presented for the existence of an optimal control for a
system described by stochastic differential equations, the solutions of which are defined for …

1. Introduction. Let us begin by recalling a theorem which insur an optimal control exists for a
rather general class of deterministic p Using vector notation, let X=(Xx,••• Xn), U=(f/i,••• Uk) …

Stochastic optimal control problems are usually analyzed under one of three types of
assumptions: a) Countability assumptions on the underlying probability space—this …

1. Introduction. The purpose of this paper is to extend methods of dynamic programming to
very general types of continuous time stochastic control systems. The controlled processes …

There are usually two ways to study optimal stochastic control problems: Pontryagin's
maximum principle and Bellman's dynamic programming, involving an adjoint process ψ …