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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Explosion problems for symmetric diffusion processes


Author: Kanji Ichihara
Journal: Trans. Amer. Math. Soc. 298 (1986), 515-536
MSC: Primary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1986-0860378-9
MathSciNet review: 860378
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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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DOI: https://doi.org/10.1090/S0002-9947-1986-0860378-9
Article copyright: © Copyright 1986 American Mathematical Society