Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise |
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Authors: | S. Albeverio,V. Mandrekar,B. Rü diger |
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Affiliation: | 1. Institut für Angewandte Mathematik der Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany;2. SFB 611, Germany;3. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA;4. Mathematisches Institut, Universität Koblenz-Landau, Campus Koblenz, Universitätsstrasse 1, 56070 Koblenz, Germany |
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Abstract: | Existence and uniqueness of the mild solutions for stochastic differential equations for Hilbert valued stochastic processes are discussed, with the multiplicative noise term given by an integral with respect to a general compensated Poisson random measure. Parts of the results allow for coefficients which can depend on the entire past path of the solution process. In the Markov case Yosida approximations are also discussed, as well as continuous dependence on initial data, and coefficients. The case of coefficients that besides the dependence on the solution process have also an additional random dependence is also included in our treatment. All results are proven for processes with values in separable Hilbert spaces. Differentiable dependence on the initial condition is proven by adapting a method of S. Cerrai. |
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Keywords: | 60H05 60G51 60G57 46B09 47G99 |
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