Construction of Generalized Diffusion Processes: the Resolvent Approach

Ying LI, Yong Hua MAO

Acta Mathematica Sinica ›› 2020, Vol. 36 ›› Issue (6) : 691-710.

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Acta Mathematica Sinica ›› 2020, Vol. 36 ›› Issue (6) : 691-710. DOI: 10.1007/s10114-020-9282-8
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Construction of Generalized Diffusion Processes: the Resolvent Approach

  • Ying LI1, Yong Hua MAO2
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Abstract

In this paper, we define the generalized diffusion operator L=d/dM d/dS for two suitable measures on the line, which includes the generators of the birth-death processes, the one-dimensional diffusion and the gap diffusion among others. Via the standard resolvent approach, the associated generalized diffusion processes are constructed.

Key words

Generalized diffusion operator / birth-death processes / diffusion / gap diffusion / resolvent / generalized diffusion processes

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Ying LI, Yong Hua MAO. Construction of Generalized Diffusion Processes: the Resolvent Approach. Acta Mathematica Sinica, 2020, 36(6): 691-710 https://doi.org/10.1007/s10114-020-9282-8

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Funding

Supported in part by NSFC (Grant No. 11771047) and Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong ChengChuang Xin Ren Cai (Grant No. 2019RS1057)

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