## Abstract

We show that the only flow solving the stochastic differential equation (SDE) on R (Formula presented.), where W^{+} and W^{-} are two independent white noises, is a coalescing flow we will denote by Pdbl^{±}. tHE FLOW Pdbl^{±} is aWiener solution of the SDE. Moreover, K^{+} = (Formula presented.) is the unique solution (it is also a Wiener solution) of the SDE (Formula presented) for s < t, x ∈ ℝ and f a twice continuously differentiable function. A third flow Pdbl^{+} can be constructed out of the n-point motions of K^{+} This flow is coalescing and its n-point motion is given by the n-point motions of K^{+} up to the first coalescing time, with the condition that when two points meet, they stay together. We note finally that K^{+} = (Formula presented.).

Original language | English (US) |
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Pages (from-to) | 1323-1346 |

Number of pages | 24 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 50 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1 2014 |

## Keywords

- Arratia flow or Brownian web
- Brownian motion with oblique reflection on a wedge
- Coalescing flow
- Stochastic flows

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty