Lévy driven CARMA generalized processes and stochastic partial differential equations |
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| Institution: | 1. Department of Industrial & Systems Engineering, National University of Singapore, and IPS Research Center, Waseda University, Japan;2. College of Mathematics & Computer Science, Hebei University, China |
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| Abstract: | We give a new definition of a Lévy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of our SPDE. Our model unifies all known definitions of CARMA random fields, and in particular for dimension 1 we obtain the classical CARMA process. |
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| Keywords: | Infinitely divisible distributions Lévy white noise Stochastic partial differential equations Generalized stochastic processes |
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