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- W1619095666 abstract "AbstractIn the paper we study stochastic convolution appearing in Volterra equationdriven by so called L´evy process. By L´evy process we mean a process with homo-geneous independent increments, continuous in probability and cadlag. 1 Introduction Let H be a real separable Hilbert space with an inner product h·,·i H and a norm | · | H .In the paper we consider a stochastic version of linear, scalar type Volterra equation inH of the formu(t) =Z t0 a(t− τ)Au(τ)dτ +x+g(t), t ≥ 0, (1)where a ∈ L 1loc (R + ), A is an unbounded linear operator in H with a dense domain D(A),g is an H-valued mapping and x ∈ H.The linear integral equation (1) is a subject of many papers connected with appli-cations in different fields. Among others, the equation (1) may be applied to severalproblems arising in mathematical physics. For instance, theory of viscoelasticity providesnumerous problems leading to the Volterra equation of the form (1) (see [9], for survey). Key words and phrases: stochastic Volterra equation, L´evy process, stochastic convolution2001 Mathematics Subject Classification: primary: 60H20; secondary: 60G51, 60H05." @default.
- W1619095666 created "2016-06-24" @default.
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- W1619095666 date "2004-11-07" @default.
- W1619095666 modified "2023-09-27" @default.
- W1619095666 title "Stochastic Volterra convolution with Lévy process" @default.
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