Nonlinear diffusion with jumps

Carl Graham

Annales de l'I.H.P. Probabilités et statistiques (1992)

  • Volume: 28, Issue: 3, page 393-402
  • ISSN: 0246-0203

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Graham, Carl. "Nonlinear diffusion with jumps." Annales de l'I.H.P. Probabilités et statistiques 28.3 (1992): 393-402. <http://eudml.org/doc/77439>.

@article{Graham1992,
author = {Graham, Carl},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting particle systems; propagation of chaos; McKean-Vlasov diffusions with jumps; nonlinear martingale problems; coupling},
language = {eng},
number = {3},
pages = {393-402},
publisher = {Gauthier-Villars},
title = {Nonlinear diffusion with jumps},
url = {http://eudml.org/doc/77439},
volume = {28},
year = {1992},
}

TY - JOUR
AU - Graham, Carl
TI - Nonlinear diffusion with jumps
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1992
PB - Gauthier-Villars
VL - 28
IS - 3
SP - 393
EP - 402
LA - eng
KW - interacting particle systems; propagation of chaos; McKean-Vlasov diffusions with jumps; nonlinear martingale problems; coupling
UR - http://eudml.org/doc/77439
ER -

References

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  1. [1] N. El-Karoui and J.-P. Lepeltier, Représentation des processus ponctuels multi-variés à l'aide d'un processus de Poisson, Z. Wahrsch. Verw. Geb., Vol. 39, 1977, pp. 111-133. Zbl0359.60065MR448546
  2. [2] A. Gerardi and M. Romiti, A Discrete Non-Linear Markov Model for a Population of Interacting Cells, Stoch. Proc. Appl., Vol. 37, 1991, pp. 33-43. Zbl0725.60090MR1091692
  3. [3] C. Graham, Nonlinear Limit for a System of Diffusing Particles which Alternate between two states, Appl. Math. Optim., Vol. 22, 1990, pp. 75-90. Zbl0707.60072MR1046696
  4. [4] C. Graham, McKean-Vlasov Ito-Shorohod Equations, and Nonlinear Diffusions with Discrete Jump Sets, Stoch. Proc. Appl., Vol. 40, 1992, pp. 69-82. Zbl0749.60096MR1145460
  5. [5] C. Graham and M. Métivier, System of Interacting Particles and Nonlinear Diffusion in a Domain with Sticky Boundary, Probab. Theory Rel. Fields., Vol. 82, 1989, pp. 225-240. Zbl0687.60087MR998932
  6. [6] H.P. Mckean, Fluctuations in the Kinetic Theory of Gases, Comm. Pure Appl. Math., Vol. 28, 1975, pp. 435-455. MR395662
  7. [7] D. Pollard, Convergence of Stochastic Processes, Springer, New York, 1984. Zbl0544.60045MR762984
  8. [8] T. Shiga and H. Tanaka, Central Limit Theorem for a System of Markovian Particules with Mean-Field Interaction, Z. Wahrsch. Verw. Geb., Vol. 69, 1984, pp. 439-459. Zbl0607.60095MR787607
  9. [9] A.-S. Sznitman, Equations de type de Boltzmann, spatialement homogènes, Z. Wahrsch. Verw. Geb., Vol. 66, 1984, pp. 559-592. Zbl0553.60069MR753814
  10. [10] A.-S. Sznitman, Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, J. Funct. Anal., Vol. 56, 3, 1984, pp. 311-336. Zbl0547.60080MR743844
  11. [11] H. Tanaka, Probabilistic Treatment of the Boltzmann Equation for Maxwellian Molecules, Z. Wahrsch. Verw. Geb., Vol. 46, 1978, pp. 67-105. Zbl0389.60079MR512334
  12. [12] V.M. Zolotarev, Probability Metrics, Theory Prob. Appl., Vol. 28, 2, 1983, pp. 278-302. Zbl0533.60025MR700210

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