Strong solutions of non-colliding particle systems
Abstract
We study systems of stochastic differential equations describing positions x1,x2,...,xp of p ordered particles, with inter-particles repulsions of the form Hij(xi,xj)/(xi-xj). We show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point x1(0)≤ ...≤ xp(0) in the whole generality, under natural assumptions on the coefficients of the equations.
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