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We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.
In this paper we obtain a closed form expression of the expected exit time of a Brownian motion from equilateral triangles. We consider first the analogous problem for a symmetric random walk on the triangular lattice and show that it is equivalent to the ruin problem of an appropriate three...
In this paper we discuss the controllability of a wave equation with random noise. Our main tools are the Ito representation theorem and an adaptation of the Hilbert uniqueness method for the exact controllability of deterministic equations.
We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming approach. We prove local optimality principles for viscosity super- and subsolutions of degenerate Hamilton–Jacobi equations in a very general setting. We...
Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L \infty norm and in the L 1 norm. We consider such optimization problems. We derive the Euler–Lagrange equations, and...
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