Stochastic evolution equations with Volterra noise

Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...

Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

Stochastic evolution equations with multiplicative noise

We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a C0−semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise analysis. We prove existence and uniqueness of solutions for this class of SPDEs. In particular, we al...

Stochastic Volterra integral equations with a parameter

Volterra Equations with Fractional Stochastic Integrals

We assume that a probability space (Ω,η,P) is given, where Ω denotes the space C(R+, Rk) equipped with the topology of uniform convergence on compact sets, η the Borel σ-field of Ω, and P a probability measure on Ω. Let {Wt(ω) = ω(t), t ≥ 0} be a Wiener process. For any t ≥ 0, we define ηt = σ{ω(s); s < t}∨Z, where Z denotes the class of the elements in ηt which have zero P-measure. Pardoux and...