Lenses in skew Brownian flow.(English)Zbl 1071.60073

Lenses in a skew Brownian flow are investigated. In this stochastic flow individual particles follow skew Brownian flow with each one of these processes is driven by the same Brownian motion, i.e. $$X^{s,x}_t=x + B_t - B_s + \beta L^{s,x}_t ,$$ where $$B$$ is a Brownian motion, $$L$$ is the local time of $$X$$. The authors present qualitative and distributional results on lenses and bifurcation times (ordinary, semi-flat, anticipated). This paper is the continuation of papers on skew Brownian flows [see M. Barlow, the authors and A. Mandelbaum, in: Séminaire de probabilités XXXV. Lect. Notes Math. 1755, 202–205 (2001; Zbl 0977.60074); K. Burdzy and Z.-Q. Chen, Ann. Probab. 29, 1693–1715 (2001; Zbl 1037.60057)].

MSC:

 60J65 Brownian motion 60J55 Local time and additive functionals 60G17 Sample path properties 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Citations:

Zbl 0977.60074; Zbl 1037.60057
Full Text:

References:

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