Brownian beads
We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Itô's excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a functio...
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| Veröffentlicht in: | Probability theory and related fields 2003-11, Vol.127 (3), p.367-387 |
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| container_title | Probability theory and related fields |
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| creator | VIRAG, Balint |
| description | We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Itô's excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2. |
| doi_str_mv | 10.1007/s00440-003-0289-8 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0178-8051 |
| ispartof | Probability theory and related fields, 2003-11, Vol.127 (3), p.367-387 |
| issn | 0178-8051 1432-2064 |
| language | eng |
| recordid | cdi_proquest_journals_2661265730 |
| source | Business Source Complete; Springer Nature - Complete Springer Journals |
| subjects | Beads Brownian motion Conformal mapping Exact sciences and technology Markov processes Mathematics Parametric inference Probability Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistical analysis Statistics Theorems |
| title | Brownian beads |
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