Properties of switching jump diffusions: Maximum principles and Harnack inequalities Article Swipe

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Mathematics Harnack's inequality Jump diffusion Jump Stochastic differential equation Harnack's principle Maximum principle Applied mathematics Class (philosophy) Work (physics) Diffusion Inequality Jump process Mathematical analysis Statistical physics Mathematical economics Mathematical optimization Computer science Thermodynamics Optimal control Physics Artificial intelligence Quantum mechanics

Xiaoshan Chen , Zhen-Qing Chen , Ky Tran , George Yin ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3150/17-bej1012 · OA: W2963220151

This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated operators for switching jump diffusions are non-local, resulting in more difficulty in treating such systems. Our study is carried out by taking into consideration of the interplay of stochastic processes and the associated systems of integro-differential equations.