Title | On the McKean–Vlasov equation with infinite mass |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Tantsiura, MV |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2016.08.019 |
Issue | 8 |
Section | Mathematics |
Pagination | 19-25 |
Date Published | 8/2016 |
Language | Ukrainian |
Abstract | We consider infinite systems of stochastic differential equations that describe the motion of interacting particles in a random environment. Theorems on existence and uniqueness of the solution are proved. We also obtain a limit theorem for corresponding measure-valued processes in the case where the mass of each particle tends to zero, and the density of particles grows to infinity. |
Keywords | McKean–Vlasov equation, measure-valued processes |
References:
- Sznitman A.S. Ecole d'Ete de Probabilites de Saint-Flour XIX – 1989, Lecture Notes in Mathematics, Vol. 1464, Berlin: Springer, 1991: 165–251. https://doi.org/10.1007/BFb0085169
- McKean H.P. Proc. Nat. Acad. Sci. USA, 1966, 56: 1907–1911. https://doi.org/10.1073/pnas.56.6.1907
- Kac M. Proc. Third Berkeley Symp. on Math. Statist. and Prob., Vol. 3, Berkeley: Univ. of Calif. Press, 1956: 171–197.
- Dawson D. A. Ecole d'Ete de Probabilites de Saint-Flour XXI – 1991, Lecture Notes in Mathematics, Vol. 1541, Berlin: Springer, 1993: 1–260. https://doi.org/10.1007/BFb0084190
- Friedman A. Partial differential equations of parabolic type, Englewood Cliffs, N.J.: Prentice-Hall, 1964.
- Veretennikov A. J. Mathematics of the USSR-Sbornik, 1981, 39, No 3: 387–403. https://doi.org/10.1070/SM1981v039n03ABEH001522
- Skorokhod A.V. Studies in the theory of random processes, Reading, Mass: Addison-Wesley, 1965.