Strong solutions of non-colliding particle systems

Abstract : 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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Submitted on : Wednesday, July 16, 2014 - 11:43:09 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM
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Piotr Graczyk, Jacek Malecki. Strong solutions of non-colliding particle systems. 2014. ⟨hal-01023820⟩

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