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The Noise Made by a Poisson Snake
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Jon Warren, University of Warwick
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Abstract
The purpose of this article is to study a coalescing
flow of sticky Brownian motions. Sticky Brownian motion arises as a weak
solution of a stochastic differential equation, and the study of the flow
reveals the nature of the extra randomness that must be added to the driving
Brownian motion. This can be represented in terms of Poissonian marking
of the trees associated with the excursions of Brownian motion. We also
study the noise, in the sense of Tsirelson, generated by the flow. It is
shown that this noise is not generated by any Brownian motion, even though
it is predictable.
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Full text: PDF
Pages: 1-21
Published on: September 2, 1999
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Electronic Journal of Probability. ISSN: 1083-6489 |
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