Displaying similar documents to “Some results on stochastic convolutions arising in Volterra equations perturbed by noise”

Stochastic viability and a comparison theorem

Anna Milian (1995)

Colloquium Mathematicae

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We give explicit necessary and sufficient conditions for the viability of polyhedrons with respect to Itô equations. Using the viability criterion we obtain a comparison theorem for multi-dimensional Itô processes

Existence and uniqueness of solutions for non-linear stochastic partial differential equations.

Tomás Caraballo Garrido (1991)

Collectanea Mathematica

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We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t,x(t)) + B(t,x(a(t))) + f(t)dt = (C(t,x(b(t)) + g(t))dwt, where A(t,·), B(t,·) and C(t,·) are suitable families of non linear operators in Hilbert spaces, wt is a Hilbert valued Wiener process, and a, b are functions of delay. If A satisfies a coercivity condition and a monotonicity hypothesis, and if B, C are Lipschitz...