Jump measure densities corresponding to Brownian motion on an annulus
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We consider the jump measure densities for Dirichlet forms of a non-local type corre- sponding to the skew product diffusion processes of a one dimensional diffusion process on R and the spherical Brownian motion on Sd-1. In , we showed a limit theorem for the Dirichlet forms of local type to that of non-local type, in view of semi groups for time changes of these skew product . Further, the Dirichlet forms corresponding to the limit processes are obtained in . The Dirichlet form corresponding to the limit process has a diffusion part, a jump part, and a killing part. In this paper we discuss the jump rate corresponding to the time changed skew product diffusion process of an extended Bessel process and the spherical Brownian motion. We focus on a 2 dimensional case so that the corresponding skew product diffusion processes is recurrent. We can find the effects of the recurrent property to jump rates. We clarify jump measure densities corresponding to Brownian motion on annulus.
奈良女子大学人間文化研究科年報 (33), 123-132, 2018-03-31