Displaying similar documents to “Nonlinear stochastic heat equations with cubic nonlinearities and additive Q -regular noise in ℝ 1 .”

Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions

Krystyna Twardowska

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Some generalizations of the approximation theorem of Wong-Zakai type for stochastic differential equations are examined. One of them deals with functional stochastic differential equations defined on some spaces of continuous functions. The second one concerns the situations when the state space and the Wiener process have values in some Hilbert spaces. The comparison of these results as well as some examples are also included. The correction terms computed here are then applied to the...

Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations

Anne de Bouard, Arnaud Debussche, Laurent Di Menza (2001)

Journées équations aux dérivées partielles

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We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non...