Explosion problems for symmetric diffusion processes

Ichihara, Kanji

doi:10.1090/S0002-9947-1986-0860378-9

Explosion problems for symmetric diffusion processes
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Trans. Amer. Math. Soc. 298 (1986), 515-536 Request permission

Abstract:

We discuss the explosion problem for a symmetric diffusion process. Hasminskii’s idea cannot be applied to this case. Instead, the theory of Dirichlet forms is employed to obtain criteria for conservativeness and explosion of the process. The fundamental criteria are given in terms of the $\alpha$-equilibrium potentials and $\alpha$-capacities of the unit ball centered at the origin. They are applied to obtain sufficient conditions on the coefficients of the infinitesimal generator for conservativeness and explosion.

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