Differential equations in spaces of abstract stochastic distributions |
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Authors: | I V Melnikova M A Alshanskiy |
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Abstract: | Stochastic Itô equations with additive and multiplicative noise in separable Hilbert spaces are studied by reducing them to differential-operator equations in spaces of generalized Hilbert space-valued random variables. Results on the existence and uniqueness of solutions in these spaces are obtained by using the S-transform technique and methods of the theory of semigroups of linear operators. |
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