Feeling boundary by Brownian motion in a ball
Keyword(s):
We establish short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. So far, such results were only known in simple cases where explicit formulae are available, i.e., for sets as half-line, interval and their products. Presented asymptotics may be considered as a complement or a generalization of the famous “principle of not feeling the boundary” in case of a ball. Following the metaphor, the principle reveals when the process does not feel the boundary, while we describe what happens when it starts feeling the boundary.
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2004 ◽
Vol 20
(2)
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1993 ◽
Vol 45
(3)
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pp. 537-553
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Keyword(s):
2018 ◽
Vol 55
(2)
◽
pp. 371-394
1989 ◽
Vol 20
(5)
◽
pp. 1109-1127
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