Semimartingales from the Fokker-Planck equation

Applied Mathematics and Optimization

Volumn 53, Issue 2, 2006, Pages 209-219

  Mikami, Toshio ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Fokker Planck equation; Marginals

Indexed keywords

VECTORS;

FOKKER-PLANCK EQUATION; INTEGRABLE DRIFT VECTOR; MARGINALS;

NONLINEAR EQUATIONS;

EID: 32944481411     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00245-005-0844-z     Document Type: Article

References (23)

1. Blumenthal RM, Corson HH (1972) On continuous collections of measures. In Le Cam L, Neyman J, Scott EL (eds), Proc 6th Berkeley Sympos Math Statist Probab 2, Berkeley, 1970/1971. University of California Press, Berkeley, CA, pp 33-40
2. Carlen EA (1984) Conservative diffusions. Commun Math Phys 94:293-315
3. Cattiaux P, Léonard C (1994) Minimization of the Kullback information of diffusion processes. Ann Inst H Poincaré Probab Statist 30:83-132
4. Cattiaux P, Léonard C (1995) Correction to "Minimization of the Kullback information of diffusion processes." Ann Inst H Poincaré Probab Statist 31:705-707
5. Cattiaux P, Léonard C (1995) Large deviations and Nelson processes. Forum Math 7:95-115
6. Cattiaux P, Léonard C (1996) Minimization of the Kullback information for some Markov processes. In Azema J, Emery M, Yor M. (eds), Séminaire de Probabilités, XXX. Lecture Notes in Mathematics, Vol 1626. Springer-Verlag, Berlin, pp 288-311
7. Doob JL (1984) Classical potential theory and its probabilistic counterpart. Springer-Verlag, Berlin
8. Fleming WH, Soner HM (1993) Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, Berlin
9. Jacod J, Shiryaev AN (1987) Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin
10. Kellerer HG (1984) Duality theorems for marginal problems. Z Wahrsch Verw Gebiete 67:399-432
11. Liptser RS, Shiryaev AN (1977) Statistics of Random Processes I. Springer-Verlag, Berlin
12. Mikami T (1990) Variational processes from the weak forward equation. Commun Math Phys 135:19-40
13. Mikami T (1999) Markov marginal problems and their applications to Markov optimal control. In McEneaney WM, Yin GG, Zhang Q (eds), Stochastic Analysis, Control, Optimization and Applications, A Volume in Honor of WH Fleming. Birkhäuser, Boston, MA, pp 457-476
14. Mikami T (2000) Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric. Appl Math Optim 42:203-227
15. Mikami T (2002) Optimal control for absolutely continuous stochastic processes and the mass transportation problem. Electron Comm Probab 7:199-213
16. Mikami T (2004) Monge's problem with a quadratic cost by the zero-noise limit of h-path processes. Probab Theory Related Fields 129:245-260
17. Mikami T (to appear) A simple proof of the duality theorem for the Monge-Kantorovich Problem. Kodai Math J
18. Mikami T, Thieullen M (2004) Duality Theorem for Stochastic Optimal Control Problem. Hokkaido University Preprint Series, #652
19. Mikami T, Thieullen M (2005) Optimal Transportation Problem by Stochastic Optimal Control. Hokkaido University Preprint Series, #690
20. Nelson E (1967) Dynamical theories of Brownian Motion. Princeton University Press, Princeton, NJ
21. Rachev ST, Rüschendorf L (1998) Mass Transportation Problems, Vols I and II. Springer-Verlag, Berlin
22. Villani C (2003) Topics in Optimal Transportation. American Mathematical Society, Providence, RI
23. Zheng WA (1985) Tightness results for laws of diffusion processes application to stochastic mechanics. Ann Inst Henri Poincaré 21:103-124 (23)