Displaying similar documents to “On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.”

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...

Some results on stochastic convolutions arising in Volterra equations perturbed by noise

Philippe Clément, Giuseppe Da Prato (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Regularity of stochastic convolutions corresponding to a Volterra equation, perturbed by a white noise, is studied. Under suitable assumptions, hölderianity of the corresponding trajectories is proved.