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On the Time for Brownian Motion to Visit Every Point on a Circle

Probability 2016-05-12 v2

Abstract

Consider a Wiener process WW on a circle of circumference LL. We prove the rather surprising result that the Laplace transform of the distribution of the first time, θL\theta_L, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.

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Cite

@article{arxiv.1312.4632,
  title  = {On the Time for Brownian Motion to Visit Every Point on a Circle},
  author = {Philip Ernst and Larry Shepp},
  journal= {arXiv preprint arXiv:1312.4632},
  year   = {2016}
}

Comments

8 pages, 1 figure