Measure-valued solutions for stochastic differential equations on Hilbert Spaces driven by L\'evy measure and their optimal control
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In this paper we consider a general class of nonlinear stochastic differential equations on Hilbert spaces determined by nonstandard infinitesimal generators (drift, diffusion, jump-kernel) and driven by L\'evy process (measure). The infinitesimal generators are assumed to be only continuous and bounded on bounded sets. Under such relaxed assumptions, these equations do not have solutions in the usual sense (classical, strong, mild and weak). We prove existence of measure-valued solutions and consider several control problems (including control of the range of vector measures) and prove existence of partially observed optimal feedback controls. This paper is an extension of our previous studies on similar problems for deterministic as well as stochastic differential equations driven by cylindrical Brownian motion.
Abstract
In this paper we consider a general class of nonlinear stochastic differential equations on Hilbert spaces determined by nonstandard infinitesimal generators (drift, diffusion, jump-kernel) and driven by L\'evy process (measure). The infinitesimal generators are assumed to be only continuous and bounded on bounded sets. Under such relaxed assumptions, these equations do not have solutions in the usual sense (classical, strong, mild and weak). We prove existence of measure-valued solutions and consider several control problems (including control of the range of vector measures) and prove existence of partially observed optimal feedback controls. This paper is an extension of our previous studies on similar problems for deterministic as well as stochastic differential equations driven by cylindrical Brownian motion.
참고문헌 (21)
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