Asymptotics for the Wiener Sausage among Poissonian Obstacles |
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Authors: | Ryoki Fukushima |
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Institution: | (1) Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a
ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment
asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory
of Brownian motion almost fills the confinement ball. |
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Keywords: | Brownian motion Poissonian obstacles Wiener sausage |
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