Dr. Tomoyuki Ichiba (PSTAT)

Title: Planar Diffusions with rank-based characteristics

Abstract: We construct a diffusion process with values in the plane and with rank-based drift/dispersive characteristics. We compute the transition probabilities of this process and the order statistics, discuss pathwise uniqueness and strength of related stochastic differential equations, and study its dynamics under a time-reversal. We also show that the planar diffusion can be represented in terms of one-dimensional diffusion with bang-bang drift driven by a standard Brownian motion, its local time accumulated at the origin, and an independent standard Brownian motion, in a form which can be construed as a two-dimensional analogue of the stochastic equation satisfied by the so-called skew Brownian motion. This is a joint work with E. Robert Fernholz, Ioannis Karatzas, and Vilmos Prokaj.