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Stochastic generalized porous media equations with Lévy jump

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In this paper, we first prove the existence and uniqueness of a general stochastic differential equation in finite dimension, then extend the result to the infinite dimension by the classical Galerkin method. As an application, we prove the existence and uniqueness of the generalized stochastic porous medium equation perturbed by Lévy process.

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Correspondence to Guo Li Zhou.

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Supported by National Nature Science Foundation of China (Grant Nos. 10671212, 90820302) and Fundamental Research Funds for the Central Universities (Grant No. CDJRC10100011)

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Zhou, G.L., Hou, Z.T. Stochastic generalized porous media equations with Lévy jump. Acta. Math. Sin.-English Ser. 27, 1671–1696 (2011).

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