Strong solutions of non-colliding particle systems

We study systems of stochastic differential equations describing positions $x_1,x_2,\ldots,x_p$ of $p$ ordered particles, with inter-particles repulsions of the form $\displaystyle{\frac{H_{ij}(x_i,x_j)}{x_i-x_j}}$. We show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point $x_1(0)\leq \ldots\leq x_p(0)$ in the whole generality, under natural assumptions on the coefficients of the equations.

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