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The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as structurally difficult to solve as the original...
Impulsive control of continuous-time Markov processes with risk- sensitive long-run average cost is considered. The most general impulsive control problem is studied under the restriction that impulses are in dyadic moments only. In a particular case of additive cost for impulses, the impulsive...
In this article we consider a polygonal approximation to the unnormalized conditional measure of a filtering problem, which is the solution of the Zakai stochastic differential equation on measure space. An estimate of the convergence rate based on a distance which is equivalent to the weak...
We establish existence and comparison theorems for a class of Hamilton—Jacobi equations. The class of Hamilton—Jacobi equations includes and is broader than those studied in  We apply the existence and uniqueness results to characterizing the value functions associated with the optimal...
The solvability of forward—backward stochastic differential equations (FBSDEs for short) has been studied extensively in recent years. To guarantee the existence and uniqueness of adapted solutions, many different conditions, some quite restrictive, have been imposed. In this paper we propose a...
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint...
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