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Strong solutions of non-colliding particle systems. (English) Zbl 1307.60079
Summary: We study systems of stochastic differential equations describing positions $$x_1,\cdots,x_p$$ of $$p$$ ordered particles, with inter-particles repulsions of the form $$\frac{H_{ij}(x_i,x_j)}{(x_i-x_j)}$$. We show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point $$x_1(0) \leq \cdots \leq x_p(0)$$ in whole generality, under natural assumptions on the coefficients of the equations.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J60 Diffusion processes
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