Abstract
In this paper, we define the generalized diffusion operator \(L = {d \over {dM}}{d \over {dS}}\) 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.
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Supported in part by NSFC (Grant No. 11771047) and Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai (Grant No. 2019RS1057)
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Li, Y., Mao, Y.H. Construction of Generalized Diffusion Processes: the Resolvent Approach. Acta. Math. Sin.-English Ser. 36, 691–710 (2020). https://doi.org/10.1007/s10114-020-9282-8
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DOI: https://doi.org/10.1007/s10114-020-9282-8
Keywords
- Generalized diffusion operator
- birth-death processes
- diffusion
- gap diffusion
- resolvent
- generalized diffusion processes