Electronic Journal of Probability

Strong solutions of non-colliding particle systems

Piotr Graczyk and Jacek Małecki

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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 />

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 119, 21 pp.

Accepted: 20 December 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60H15: Stochastic partial differential equations [See also 35R60]

stochastic differential equation strong solution non-colliding particle system

This work is licensed under a Creative Commons Attribution 3.0 License.


Graczyk, Piotr; Małecki, Jacek. Strong solutions of non-colliding particle systems. Electron. J. Probab. 19 (2014), paper no. 119, 21 pp. doi:10.1214/EJP.v19-3842. https://projecteuclid.org/euclid.ejp/1465065761

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