On Conditioning Brownian Particles to Coalesce

arxiv（2023）

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摘要

We introduce the notion of a conditional distribution to a zero-probability event in a given direction of approximation and prove that the conditional distribution of a family of independent Brownian particles to the event that their paths coalesce after the meeting coincides with the law of a modified massive Arratia flow, defined in Konarovskyi (Ann Probab 45(5):3293–3335, 2017. https://doi.org/10.1214/16-AOP1137 ).

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关键词

Regular conditional probability,Modified massive Arratia flow,Cylindrical Wiener process,Coalescing Brownian motions

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