Stochastic ranking process with time dependent intensities
Hariya, Yuu ; Hattori, Kumiko ; Hattori, Tetsuya ; Nagahata, Yukio ; Takeshima, Yuusuke ; Kobayashi, Takahisa
Tohoku Math. J. (2), Tome 63 (2011) no. 1, p. 77-111 / Harvested from Project Euclid
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.
Publié le : 2011-05-15
Classification:  Stochastic ranking process,  move-to-front rules,  least-recently-used caching,  hydrodynamic limit,  inviscid Burgers equation with evaporation,  Poisson random measure,  60K35,  35C05,  82C22
@article{1303219937,
     author = {Hariya, Yuu and Hattori, Kumiko and Hattori, Tetsuya and Nagahata, Yukio and Takeshima, Yuusuke and Kobayashi, Takahisa},
     title = {Stochastic ranking process with time dependent intensities},
     journal = {Tohoku Math. J. (2)},
     volume = {63},
     number = {1},
     year = {2011},
     pages = { 77-111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303219937}
}
Hariya, Yuu; Hattori, Kumiko; Hattori, Tetsuya; Nagahata, Yukio; Takeshima, Yuusuke; Kobayashi, Takahisa. Stochastic ranking process with time dependent intensities. Tohoku Math. J. (2), Tome 63 (2011) no. 1, pp.  77-111. http://gdmltest.u-ga.fr/item/1303219937/