Stochastic evolution equations driven by cylindrical stable 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...

Stochastic Volterra equations driven by cylindrical Wiener process

In this paper, stochastic Volterra equations driven by cylindrical and genuine Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given. The key role is played by convergence of α-times resolvent families.

Stochastic Resonance in Chua’s Circuit Driven by Alpha-stable Noise

On One-dimensional Stochastic Equations Driven by Symmetric Stable Processes

We study stochastic equations Xt = x0 + ∫ t 0 b(u,Xu−) dZu, where Z is an one-dimensional symmetric stable process of index α with 0 < α ≤ 2, b : [0,∞) × IR → IR is a measurable diffusion coefficient, and x0 ∈ IR is the initial value. We give sufficient conditions for the existence of weak solutions. Our main results generalize results of P. A. Zanzotto [18] who dealt with homogeneous diffusion...

Stochastic Partial Differential Equations Driven by Purely Spatial Noise

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron–Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...