Stochastic ranking process with time dependent intensities

Details Stochastic ranking process with time dependent intensities Stochastic ranking process with time dependent intensities

2010-10-25

arxiv.org/abs/1010.5045v1

Tohoku Mathematical Journal 63 (2011) 77-111

Mathematics

Probability

Scientific paper

We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the infinite particle limit. We give an explicit formula for the limit distribution and show that the limit distribution function is a unique global classical solution to an initial value problem for a system of a first order non-linear partial differential equations with time dependent coefficients.

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