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Seminars

Strong solutions of stochastic equations with rank-based coefficients and local times

Hold Date
2015-12-11 17:45〜2015-12-11 18:45
Place
Seminar Room W1-C-616, West Zone 1, Ito campus, Kyushu University
Object person
 
Speaker
Tomoyuki Ichiba (University of California Santa Barbara)

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.