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On a fractional SPDE driven by fractional noise and a pure jump Lévy noise in \(\mathbb{R}^d\). (English) Zbl 1474.60166

Summary: We study a stochastic partial differential equation in the whole space \(x \in \mathbb{R}^d\), with arbitrary dimension \(d \geq 1\), driven by fractional noise and a pure jump Lévy space-time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R11 Fractional partial differential equations
35R60 PDEs with randomness, stochastic partial differential equations
60J76 Jump processes on general state spaces
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