Geodesic
Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 25 (2005) no. 1, pp. 129-157.

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In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended to cover Borel measurable drift and diffusion which are assumed to be bounded on bounded sets. Also we consider control problems for these systems and present several results on the existence of optimal feedback controls.
Keywords: stochastic differential equations, Hilbert space, measurable vector fields, finitely additive measure solutions, optimal feedback controls 
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Ahmed, N. Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 25 (2005) no. 1, pp. 129-157. http://geodesic.mathdoc.fr/item/DMDICO_2005_25_1_a6/

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