Strong solutions of non-colliding particle systems

Abstract

We study systems of stochastic differential equations describing positions $x_1,...,x_p$ of $p$ ordered particles, with inter-particles repulsions of the form $H_{ij}(x_i,x_j)/(x_i-x_j)$. We show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point $x_1(0) \leq ... \leq x_p(0)$ in the whole generality, under natural assumptions on the coefficients of the equations.<br /><br />