On Conditioning Brownian Particles to Coalesce

Vitalii Konarovskyi () and Victor Marx ()
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Vitalii Konarovskyi: Universitätsstraße 25
Victor Marx: Universität Leipzig

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2126-2164

Abstract: Abstract 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 ).

Keywords: Regular conditional probability; Modified massive Arratia flow; Cylindrical Wiener process; Coalescing Brownian motions; Primary 60E05; 60J90; Secondary 60G15; 60G44; 60K35 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01267-4

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