We apply the semigroup setting of Desch and Miller to a class of stochastic integral equations of Volterra type with completely monotone kernels with a multiplicative noise term; the corresponding equation is an infinite dimensional stochastic equation with unbounded diffusion operator that we solve with the semigroup approach of Da Prato and Zabczyk. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.

An analytic approach to stochastic Volterra equations with completely monotone kernels

Bonaccorsi, Stefano;Mastrogiacomo, Elisa
2009-01-01

Abstract

We apply the semigroup setting of Desch and Miller to a class of stochastic integral equations of Volterra type with completely monotone kernels with a multiplicative noise term; the corresponding equation is an infinite dimensional stochastic equation with unbounded diffusion operator that we solve with the semigroup approach of Da Prato and Zabczyk. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.
2009
2
Bonaccorsi, Stefano; Mastrogiacomo, Elisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/7191
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