where describes the law of X and dB denotes the Wiener process. That is the coefficients of the SDE depend on the marginal distribution of the process X. In general, the process can describe non-linear diffusion.[4][5]
^Des Combes, Rémi Tachet (2011). (PDF). Archived from the original (PDF) on 2012-05-11. {{cite journal}}: Cite journal requires |journal= (help)
^Funaki, T. (1984). "A certain class of diffusion processes associated with nonlinear parabolic equations". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 67 (3): 331–348. doi:10.1007/BF00535008. S2CID 121117634.
^ abMcKean, H. P. (1966). "A Class of Markov Processes Associated with Nonlinear Parabolic Equations". Proc. Natl. Acad. Sci. USA. 56 (6): 1907–1911. Bibcode:1966PNAS...56.1907M. doi:10.1073/pnas.56.6.1907. PMC220210. PMID 16591437.
^ abcCarmona, Rene; Delarue, Francois; Lachapelle, Aime. "Control of McKean-Vlasov Dynamics versus Mean Field Games" (PDF). Princeton University.
^ abChan, Terence (January 1994). "Dynamics of the McKean-Vlasov Equation". The Annals of Probability. 22 (1): 431–441. doi:10.1214/aop/1176988866. ISSN 0091-1798.
This probability-related article is a stub. You can help Wikipedia by expanding it.
mckean, vlasov, process, probability, theory, stochastic, process, described, stochastic, differential, equation, where, coefficients, diffusion, depend, distribution, solution, itself, equations, model, vlasov, equation, were, first, studied, henry, mckean, 1. In probability theory a McKean Vlasov process is a stochastic process described by a stochastic differential equation where the coefficients of the diffusion depend on the distribution of the solution itself 1 2 The equations are a model for Vlasov equation and were first studied by Henry McKean in 1966 3 Definition EditMcKean Vlasov processes take the form 3 4 d X t a X t m t d B t b X t m t d t displaystyle dX t a X t mu t dB t b X t mu t dt where m t L X t displaystyle mu t mathcal L X t describes the law of X and dB denotes the Wiener process That is the coefficients of the SDE depend on the marginal distribution of the process X In general the process can describe non linear diffusion 4 5 Applications EditMean field theory Mean field game theory 4 Random matrices including Dyson s model on eigenvalue dynamics for random symmetric matrices and the Wigner semicircle distribution 5 References Edit Des Combes Remi Tachet 2011 Non parametric model calibration in finance Calibration non parametrique de modeles en finance PDF Archived from the original PDF on 2012 05 11 a href Template Cite journal html title Template Cite journal cite journal a Cite journal requires journal help Funaki T 1984 A certain class of diffusion processes associated with nonlinear parabolic equations Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete 67 3 331 348 doi 10 1007 BF00535008 S2CID 121117634 a b McKean H P 1966 A Class of Markov Processes Associated with Nonlinear Parabolic Equations Proc Natl Acad Sci USA 56 6 1907 1911 Bibcode 1966PNAS 56 1907M doi 10 1073 pnas 56 6 1907 PMC 220210 PMID 16591437 a b c Carmona Rene Delarue Francois Lachapelle Aime Control of McKean Vlasov Dynamics versus Mean Field Games PDF Princeton University a b Chan Terence January 1994 Dynamics of the McKean Vlasov Equation The Annals of Probability 22 1 431 441 doi 10 1214 aop 1176988866 ISSN 0091 1798 This probability related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title McKean Vlasov process amp oldid 1117890085, wikipedia, wiki, book, books, library,
