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Which sets contain multiple points of Brownian motion?

Published online by Cambridge University Press:  24 October 2008

Nils Tongring
Nils Tongring
Affiliation:
Department of Mathematics, Northeastern University, Boston, MA 02115, U.S.A.
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Extract

In 1950, Dvoretzky, Erdös and Kakutani [2] showed that in ℝ3 almost all paths of Brownian motion X have double points, or self-intersections of order 2 (there are no triple points [4]); later the same authors proved that almost all sample paths of Brownian motion in the plane have points of arbitrarily high multiplicity (a point x in ℝ2 is a k-tuple point for the path ω, or a self-intersection of order k, if there are times tl < t2 < … < tk such that x = X(t1, ω) = X(t2, ω) = … X(tk, ω)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 1 , January 1988 , pp. 181 - 187
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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