Self-avoiding random walk: A Brownian motion model with local time drift |
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Authors: | J R Norris L C G Rogers David Williams |
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Institution: | (1) Statistical Laboratory, 16 Mill Lane, CB2 1SB Cambridge, Great Britain |
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Abstract: | Summary A natural model for a self-avoiding Brownian motion inR
d, when specialised and simplified tod=1, becomes the stochastic differential equation
, where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that
exists almost surely, and to identify the limit. |
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Keywords: | |
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