A1 - Karczewska, Anna
PB - Toruń: Juliusz Schauder Center for Nonlinear Studies Nicolaus Copernicus University
N2 - In the paper, two general problems concerning linear stochastic evolution equations of convolution type are studied: existence of strong solutions to such stochastic Volterra equations in a Hilbert space and regularity of solutions to two classes of stochastic Volterra equations in the spaces of tempered distributions. First, we consider Volterra equations in a separable Hilbert space H with the locally integrable kernel functions, a closed linear unbounded operator A and a cylindrical Wiener process. Our main results rely essentially on techniques using a strongly continuous family of so called resolvent operators.
N2 - The resolvent approach to stochastic Volterra equations enables us to obtain new results in an elegant way, analogously like in a semigroup case. In the remaining part of the paper we study two classes of equations of the convolution type on d-dimensional torus with values in the space of tempered distributions. We consider the existence of the solutions to the equations under consideration and next we derive the conditions under which the solutions take values in function spaces.
KW - ułamkowe równania Volterry
KW - operatory rezolwenty
KW - stochastyczna konwolucja
KW - Stochastyczne równania Volterry,
T1 - Convolution type stochastic Volterra equations