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This article is devoted to the investigation of spectral asymptotics for the second-order differential operator with transmission boundary conditions. A two-term asymptotic formula is obtained for the distribution function of eigenvalues under some assumptions not excluding the reach set of...
We consider a continuous-time stochastic control problem with partial observations. Given some assumptions, we reduce the problem in successive approximation steps to a discrete-time, complete-observation, stochastic control problem with a finite number of possible states and controls. For the...
We present a model for which certain difficulties often associated with analysis on infinite-dimensional spaces do not occur. In this situation, the convolution semigroup of Wiener measures constructed by Gross becomes a self-adjoint contraction semigroup. We generalize a facet of Sobolev theory...
In this paper the utility and the difficulties of probabilistic analysis for optimization algorithms are discussed. Such an analysis is expected to deliver valuable criteria-better than the worst-case complexity-for the efficiency of an algorithm in practice.
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