分野別セミナー

Abstract:
We shall discuss path-wise uniqueness of system of stochastic equations with rank-based coefficients and local times. The system can be seen as Brownian particles diffusing on the real line with elastic collisions as well as with bounded, measurable drift and diffusion coefficients that depend on the current configuration of particles in terms of their relative rankings. Starting from the case of two particles, we shall extend our discussion of strong solvability of the system to the cases of (finitely or infinitely) many particles. The talk is based on joint work with R. Fernholz, I. Karatzas, M. Shkolnikov and V. Prokaj.