Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669205 | Bulletin des Sciences Mathématiques | 2012 | 23 Pages |
Abstract
In this paper, we study a stochastic fractional Burgers type nonlinear equation driven by a pure jump Lévy space–time white noise with d-dimensional spatial variables x∈Rd. Our equation involves a Markovian generator of a stable-like Feller process with variable order α(x). Under certain polynomial growth conditions, we establish the existence and uniqueness of an Lp(Rd)-valued (local) solution for the initial value problem to our equation. Our approaches are essentially based on the estimates of the fundamental solution to the stable-like Markovian generator and the Lp-theory of the stochastic integral with respect to the pure jump Lévy space–time white noise.
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Mathematics (General)