Explosive solutions for stochastic differential equations driven by Lévy processes

Xing, Jiamin; Li, Yong

doi:10.1016/j.jmaa.2017.04.071

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Cited by 4 publications

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“…A different approach based on the Lyapunov function to study the explosion of the solutions was discussed by Chow and Khasminskii in [7,8]. When the driving noise is a Lévy process, Xing and Li in [32] obtained some results about the explosive solutions of stochastic differential equations.…”

Section: Introductionmentioning

confidence: 99%

Finite Time Blowup of Solutions to SPDEs with Bernstein Functions of the Laplacian

Deng¹,

Liu²,

Nane³

2020

Preprint

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The blowup in finite time of solutions to SPDEsis investigated, where ξ could be either a white noise or a colored noise and φ : (0, ∞) → (0, ∞) is a Bernstein function. The sufficient conditions on σ, ξ and the initial value that imply the non-existence of the global solution are discussed. The results in this paper generalise those in [15], where the fractional Laplacian case was considered, i.e. φ(−∆) = (−∆) α/2 (1 < α < 2).

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Section: Introductionmentioning

confidence: 99%