YMSC Probability Seminar | Skew Brownian flow: a new approach

Abstract：

The skew Brownian motion is constructed by assigning signs to Brownian excursions away from 0, each excursion being positive with probability p and negative with probability 1-p. It can equivalently (Harrison-Shepp, 1981) be seen as the strong solution of the SDE dX_t=dB_t + (2p-1) dL_t(X) where L_t(X) denotes the local time of the diffusion at 0. The skew Brownian flow as studied by Burdzy-Chen (2001) and Burdzy-Kaspi (2004) is the flow of solutions driven by the same Brownian motion but starting from any time-space point in the plane. In this talk, I will give results on the properties of meeting level processes and the exact Hausdorff dimension of bifurcation times of different types appeared in the skew Brownian flow. If time permits, I will introduce another coalescing stochastic flow, called the BESQ flow, as the key to those problems. Joint work with Elie Aïdékon and Yaolin Yu.