An analytic approach to stochastic Volterra equations with completely monotone kernels |
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Authors: | Stefano Bonaccorsi Elisa Mastrogiacomo |
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Institution: | (1) Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo, Trento, Italy |
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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.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 45D05 93E20 60H30 |
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