Geodesic
On the generalization of the McKean–Vlasov equation to the case where the total mass of particles is infinite
Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 119-129 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The McKean–Vlasov equation describing the motion of a system of particles with infinite total mass is considered. The theorem of existence and uniqueness of a solution is proved. The solution is constructed by passing to the limit from that for the systems of particles having a finite total mass.
Keywords: Motion with interaction, McKean–Vlasov equation, stochastic differential equations. 
@article{THSP_2012_18_1_a7,
     author = {M. V. Tantsiura},
     title = {On the generalization of the {McKean{\textendash}Vlasov} equation to the case where the total mass of particles is infinite},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {119--129},
     year = {2012},
     volume = {18},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a7/}
}
TY  - JOUR
AU  - M. V. Tantsiura
TI  - On the generalization of the McKean–Vlasov equation to the case where the total mass of particles is infinite
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 119
EP  - 129
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a7/
LA  - en
ID  - THSP_2012_18_1_a7
ER  - 
%0 Journal Article
%A M. V. Tantsiura
%T On the generalization of the McKean–Vlasov equation to the case where the total mass of particles is infinite
%J Teoriâ slučajnyh processov
%D 2012
%P 119-129
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a7/
%G en
%F THSP_2012_18_1_a7
M. V. Tantsiura. On the generalization of the McKean–Vlasov equation to the case where the total mass of particles is infinite. Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 119-129. http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a7/

[1] D. A. Dawson, “Measure-Valued Markov Processes”, Ecole d'Eté de Probabilitës de Saint-Flour, Lecture Notes Math., XXI, ed. P. L. Hennequin, Springer, Berlin, 1991, 1-260 | MR

[2] D. A. Dawson, J. Vaillancourt, “Stochastic McKean–Vlasov equations”, Nonlin. Diff. Equa. Appl., 2 (1995), 199–229 | DOI | MR | Zbl

[3] A. A. Dorogovtsev, “Measure-valued Markov processes and stochastic flows on abstract spaces”, Stochast. and Stochast. Reports, 2004, no. 5, 395–407 | DOI | MR | Zbl

[4] A. A. Dorogovtsev, “Stochastic flows with interaction and measure-valued processes”, Int. J. Math. Math. Sci., 2003, no. 63, 3963–3977 | DOI | MR | Zbl

[5] A. A. Dorogovtsev, Measure-Valued Processes and Stochastic Flows, Institute of Mathematics of the NAS of Ukraine, Kyiv, 2007 (in Russian) | MR | Zbl

[6] P. Kotelenez, “A class of quasilinear stochastic partial differential equations of McKean–Vlasov type with mass conservation”, Probab. Theory Related Fields, 102:2 (1995), 159–188 | DOI | MR | Zbl

[7] T. M. Liggett, Interacting Particle Systems, Springer, New York, 1985 | MR | Zbl

[8] H. P. McKean, “Propagation of chaos for a class of non-linear parabolic equations”, Stochastic Differential Equations, Lecture Series in Differential Equations, 7, 1967, 41–57 | MR

[9] A. Yu. Pilipenko, “Measure-valued diffusions and continual systems of interacting particles in random media”, Ukr. Math. J., 57:9 (2005), 1289–1301 | DOI | MR | Zbl

[10] A. V. Skorohod, Stochastic Equations for Complex Systems, Reidel, Dordrecht, 1988 | MR | Zbl

[11] A. V. Skorohod, “Measure-valued diffusion”, Ukr. Math. J., 49:3 (1997), 506–513 | DOI | MR

[12] A.-S. Sznitman, “Topics in propagation of chaos”, Ecole d'Ete de Probabilites de Saint Flour, Lecture Notes in Math., XXI, ed. P. L. Hennequin, Springer, Berlin, 1991, 165-251 | DOI | MR

[13] H. Tanaka, “Probabilistic treatment of the Boltzmann equation of Maxwellian molecules”, Z. Wahrsch. Verw. Gebiete, 46:1 (1978/79), 67–105 | DOI | MR | Zbl

[14] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968 | MR | Zbl

[15] A. V. Skorokhod, Research in Theory of Random Processes, Kyiv Univ., Kyiv, 1961 (in Russian)