-
1
-
-
0000009557
-
The Vlasov dynamics and its fluctuation in the 1/N limit of interacting particles
-
Braun, W., and Hepp, K., 1977. The Vlasov dynamics and its fluctuation in the 1/N limit of interacting particles. Comm. Math. Phy. 56:101–113.
-
(1977)
Comm. Math. Phy.
, vol.56
, pp. 101-113
-
-
Braun, W.1
Hepp, K.2
-
2
-
-
84861469661
-
The law of large numbers for self-exciting correlated defaults
-
Cvitanić, J., Ma, J., and Zhang, J., 2012. The law of large numbers for self-exciting correlated defaults. Stoch. Proc. Appl. 122:2781–2810.
-
(2012)
Stoch. Proc. Appl.
, vol.122
, pp. 2781-2810
-
-
Cvitanić, J.1
Ma, J.2
Zhang, J.3
-
3
-
-
34250144062
-
Critical dynamics and fluctuations for a mean field model of cooperative behaviour
-
Dawson, D. A., 1983. Critical dynamics and fluctuations for a mean field model of cooperative behaviour. J. Statist. Phys. 31:29–85.
-
(1983)
J. Statist. Phys.
, vol.31
, pp. 29-85
-
-
Dawson, D.A.1
-
4
-
-
0001334383
-
Symmetric statistics, Poisson point processes, and multiple Wiener integrals
-
Dynkin, E. B., and Mandelbaum, A., 1983. Symmetric statistics, Poisson point processes, and multiple Wiener integrals. Ann. Statist. 11:739–745.
-
(1983)
Ann. Statist.
, vol.11
, pp. 739-745
-
-
Dynkin, E.B.1
Mandelbaum, A.2
-
6
-
-
85028661816
-
A constructive mean field analysis of multi-population neural networks with random synaptic weights and stochastic inputs
-
Faugeras, O., Touboul, J., and Cessac, B., 2006. A constructive mean field analysis of multi-population neural networks with random synaptic weights and stochastic inputs. Frontiers in Neuroscience 31(1):1–28.
-
(2006)
Frontiers in Neuroscience
, vol.31
, Issue.1
, pp. 1-28
-
-
Faugeras, O.1
Touboul, J.2
Cessac, B.3
-
8
-
-
0040831290
-
Stochastic particle approximations for generalized Boltzmann models and convergence estimates
-
Graham, C., and Méléard, S., 1997. Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann Probab. 25:115–132.
-
(1997)
Ann Probab.
, vol.25
, pp. 115-132
-
-
Graham, C.1
Méléard, S.2
-
9
-
-
38249041273
-
Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions
-
Hitsuda, M., and Mitoma, I., 1986. Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions. J. Mult. Anal. 19:311–328.
-
(1986)
J. Mult. Anal.
, vol.19
, pp. 311-328
-
-
Hitsuda, M.1
Mitoma, I.2
-
11
-
-
70449103246
-
Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type
-
Kotelenez, P., and Kurtz, T. G., 2010. Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type. Probab. Theory Related Fields 146:189–222.
-
(2010)
Probab. Theory Related Fields
, vol.146
, pp. 189-222
-
-
Kotelenez, P.1
Kurtz, T.G.2
-
12
-
-
0000817735
-
Weak convergence of stochastic integrals and differential equations. II. Infinite-dimensional case
-
Kurtz, T. G., and Protter, P. E., 1996. Weak convergence of stochastic integrals and differential equations. II. Infinite-dimensional case. Probabilistic Models for Nonlinear Partial Differential Equations (Montecatini Terme, 1995), 197–285. Lecture Notes in Mathematics 1627. Berlin:Springer.
-
(1996)
Probabilistic Models for Nonlinear Partial Differential Equations
, pp. 197-285
-
-
Kurtz, T.G.1
Protter, P.E.2
-
13
-
-
0000273833
-
Particle representations for a class of nonlinear SPDEs
-
Kurtz, T. G., and Xiong, J., 1999. Particle representations for a class of nonlinear SPDEs. Stoch. Proc. App. 83:103–126.
-
(1999)
Stoch. Proc. App.
, vol.83
, pp. 103-126
-
-
Kurtz, T.G.1
Xiong, J.2
-
14
-
-
79955481954
-
A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems
-
Kurtz, T. G., and Xiong, J., 1999. A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems. Comm. Math. Sci. 2:325–358.
-
(1999)
Comm. Math. Sci.
, vol.2
, pp. 325-358
-
-
Kurtz, T.G.1
Xiong, J.2
-
16
-
-
0010914615
-
A class of Markov processes associated with nonlinear parabolic equations
-
McKean, H. P., 1966. A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. 56:1907–1907.
-
(1966)
Proc. Natl. Acad. Sci.
, vol.56
, pp. 1907
-
-
McKean, H.P.1
-
17
-
-
0009954021
-
Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations
-
Méléard, S., 1998. Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations. Stochastics Stochastics Rep. 63:195–195.
-
(1998)
Stochastics Stochastics Rep.
, vol.63
, pp. 195
-
-
Méléard, S.1
-
18
-
-
0000467039
-
Tightness of probabilities in C([0, 1] : S') and D([0, 1]: S')
-
Mitoma, I., 1983. Tightness of probabilities in C([0, 1] : S') and D([0, 1]: S'). Ann. Prob. 11:989–999.
-
(1983)
Ann. Prob.
, vol.11
, pp. 989-999
-
-
Mitoma, I.1
-
19
-
-
0040554658
-
A martingale approach to the law of large numbers for weakly interacting stochastic processes
-
Oelschaläger, K., 1984. A martingale approach to the law of large numbers for weakly interacting stochastic processes. Ann. Probab. 12:458–479.
-
(1984)
Ann. Probab.
, vol.12
, pp. 458-479
-
-
Oelschaläger, K.1
-
20
-
-
0000793708
-
Central limit theorem for a system of Markovian particles with mean field interactions
-
Shiga, T., and Tanaka, H., 1985. Central limit theorem for a system of Markovian particles with mean field interactions. Z. Wahr. verw. Geb. 69:439–459.
-
(1985)
Z. Wahr. verw. Geb.
, vol.69
, pp. 439-459
-
-
Shiga, T.1
Tanaka, H.2
-
22
-
-
0001293553
-
Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
-
Sznitman, A. S., 1984. Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Func. Anal. 56:311–336.
-
(1984)
J. Func. Anal.
, vol.56
, pp. 311-336
-
-
Sznitman, A.S.1
-
23
-
-
0039500106
-
Limit theorems for certain diffusion processes with interaction
-
Tanaka, H., 1984. Limit theorems for certain diffusion processes with interaction. Stochastic Analysis (Katata/Kyoto, 1982), 469--488. North-Holland Mathematics Library 32. Amsterdam, the Netherlands:North-Holland.
-
(1984)
Stochastic Analysis
-
-
Tanaka, H.1
|