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In this note, we propose two different approaches to rigorously justify a pseudoMarkov property for controlled diffusion processes which is often (explicitly or implicitly) used to prove the dynamic programming principle in the stochastic control literature. The first approach develops a sketch of proof proposed by Fleming and Souganidis . The second… (More)
In this note, we rigorously justify a conditioning argument which is often (explicitly or implicitly) used to prove the dynamic programming principle in the stochastic control literature. To this end, we set up controlled martingale problems in an unusual way.
Finite-difference approximations to an elliptic–hyperbolic system arising in vortex density models for type II superconductors are studied. The problem can be formulated as a non-local Hamilton–Jacobi equation on a bounded domain with zero Neumann boundary conditions. Monotone schemes are defined and shown to be stable. An L∞ error bound is proved for the… (More)