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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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