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Volumn 2, Issue 3, 2004, Pages 325-358

A STOCHASTIC EVOLUTION EQUATION ARISING FROM THE FLUCTUATIONS OF A CLASS OF INTERACTING PARTICLE SYSTEMS ¤

Author keywords

Central limit theorem; Euler scheme; Interacting infinite particle system; Stochastic partial differential equations

Indexed keywords


EID: 79955481954     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2004.v2.n3.a1     Document Type: Article
Times cited : (51)

References (37)
  • 1
    • 84968498705 scopus 로고
    • Rate of convergence for the Kolmogorov equation with variable coefficients
    • [1]
    • [1] Pierre Bernard, Denis Talay, and Luciano Tubaro, Rate of convergence for the Kolmogorov equation with variable coefficients, Math. Comp. 63, 555-587, 1994.
    • (1994) Math. Comp , vol.63 , pp. 555-587
    • Bernard, Pierre1    Talay, Denis2    Tubaro, Luciano3
  • 3
    • 0002455942 scopus 로고
    • Distribution function inequalities for martingales
    • [3]
    • [3] Donald L. Burkholder, Distribution function inequalities for martingales, Ann. Prob. 1, 19-42,1973.
    • (1973) Ann. Prob , vol.1 , pp. 19-42
    • Burkholder, Donald L.1
  • 4
    • 0008465809 scopus 로고
    • Propagation of chaos and McKean-Vlasov equation in duals of nuclear spaces
    • [4]
    • [4] T. Chiang, G. Kallianpur, and P. Sundar, Propagation of chaos and McKean-Vlasov equation in duals of nuclear spaces, Appl. Math. Optim. 24, 55-83, 1991.
    • (1991) Appl. Math. Optim , vol.24 , pp. 55-83
    • Chiang, T.1    Kallianpur, G.2    Sundar, P.3
  • 5
    • 0001524126 scopus 로고    scopus 로고
    • Discrete filtering using branching and inter-acting particle systems
    • [5]
    • [5] Dan Crisan, Pierre Del Moral, and Terry Lyons, Discrete filtering using branching and inter-acting particle systems, Markov Process, Related Fields 5, 293-318, 1999.
    • (1999) Markov Process, Related Fields , vol.5 , pp. 293-318
    • Crisan, Dan1    Moral, Pierre Del2    Lyons, Terry3
  • 6
    • 17744362474 scopus 로고    scopus 로고
    • Interacting particle approximations of the Kushner Stratonovich equation
    • [6]
    • [6] Dan Crisan, Piere Del Moral, and Terry Lyons, Interacting particle approximations of the Kushner Stratonovich equation, Adv. Appl. Probab. 31, 819-838, 1999.
    • (1999) Adv. Appl. Probab , vol.31 , pp. 819-838
    • Crisan, Dan1    Moral, Piere Del2    Lyons, Terry3
  • 7
    • 0032186558 scopus 로고    scopus 로고
    • Convergence of a branching particle method to the solution of the Zakai equation
    • [7]
    • [7] Dan Crisan, Jessica Gaines, and Terry Lyons, Convergence of a branching particle method to the solution of the Zakai equation, SIAM J. Appl. Math. 58, 1568-1590, 1998.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 1568-1590
    • Crisan, Dan1    Gaines, Jessica2    Lyons, Terry3
  • 8
    • 0033261066 scopus 로고    scopus 로고
    • A particle approximation to the solution of the Kushner-Stratonovitch equation
    • [8]
    • [8] Dan Crisan and Terry Lyons, A particle approximation to the solution of the Kushner-Stratonovitch equation, Probab. Theory and Related Fields 115, 549-578, 1999.
    • (1999) Probab. Theory and Related Fields , vol.115 , pp. 549-578
    • Crisan, Dan1    Lyons, Terry2
  • 10
    • 0013326015 scopus 로고
    • Non-linear filtering using random particles
    • [10]
    • [10] Pierre Del Moral, Non-linear filtering using random particles, Theory Probab. Appl. 40, 690-701, 1995.
    • (1995) Theory Probab. Appl , vol.40 , pp. 690-701
    • Moral, Pierre Del1
  • 11
    • 0012023934 scopus 로고    scopus 로고
    • On a class of discrete generation interacting particle systems
    • [11]
    • [11] P. Del Moral, M.A. Kouritzin, and L. Miclo, On a class of discrete generation interacting particle systems, Electron. J. Probab. 6, 2001.
    • (2001) Electron. J. Probab , vol.6
    • Del Moral, P.1    Kouritzin, M.A.2    Miclo, L.3
  • 12
    • 0008402311 scopus 로고
    • An approximation for the nonlinear filtering problem with error bound
    • [12]
    • [12] G.B.Di Masi, M. Pratelli, and W.J. Runggaldier, An approximation for the nonlinear filtering problem with error bound, Stochastics 14, 247-271, 1985.
    • (1985) Stochastics , vol.14 , pp. 247-271
    • Di Masi, G.B.1    Pratelli, M.2    Runggaldier, W.J.3
  • 14
    • 0010067102 scopus 로고
    • Le Gland, and Francois, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise
    • [14]
    • [14] Patrick Florchinger, Le Gland, and Francois, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise, Stochastics Rep. 35, 233-256, 1991.
    • (1991) Stochastics Rep , vol.35 , pp. 233-256
    • Florchinger, Patrick1
  • 15
    • 0010171470 scopus 로고
    • Le Gland, and Francois, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise
    • [15] in (Antibes), Lecture Notes in Control and Inform. Sci. 144, Springer, Berlin
    • [15] Patrick Florchinger, Le Gland, and Francois, Time-discretization of the Zakai equation for diffusion processes observed in correlated noise, in Analysis and optimization of systems (Antibes, 1990), 228-237, Lecture Notes in Control and Inform. Sci. 144, Springer, Berlin.
    • (1990) Analysis and optimization of systems , pp. 228-237
    • Florchinger, Patrick1
  • 16
    • 0042063585 scopus 로고
    • Le Gland, and Francois, Particle approximations for first order stochastic partial differential equations
    • [16] New Brunswick, NJ, Lecture Notes in Control and Inform. Sci. 177 Springer, Berlin, 1992
    • [16] Patrick Florchinger, Le Gland, and Francois, Particle approximations for first order stochastic partial differential equations, Appl. stochastic anal., New Brunswick, NJ, 121-133, 1991, Lecture Notes in Control and Inform. Sci. 177 Springer, Berlin, 1992.
    • (1991) Appl. stochastic anal , pp. 121-133
    • Florchinger, Patrick1
  • 18
    • 0039586201 scopus 로고
    • Nonlinear Ito-Skorohod equations and martingale problem with discrete jump sets
    • [18]
    • [18] Carl Graham, Nonlinear Ito-Skorohod equations and martingale problem with discrete jump sets, Stochastic Process Appl. 40, 69-82, 1992.
    • (1992) Stochastic Process Appl , vol.40 , pp. 69-82
    • Graham, Carl1
  • 19
    • 38249041273 scopus 로고
    • Tightness problem and stochastic evolution equationarising from °uctuation phenomena for interacting diffusions
    • [19]
    • [19] Masuyuki Hitsuda and Itaru Mitoma, Tightness problem and stochastic evolution equationarising from °uctuation phenomena for interacting diffusions, J. Multivariate Anal. 19, 311-328, 1986.
    • (1986) J. Multivariate Anal , vol.19 , pp. 311-328
    • Hitsuda, Masuyuki1    Mitoma, Itaru2
  • 20
  • 22
    • 0028500263 scopus 로고
    • Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures
    • [22]
    • [22] Gopinath Kallianpur and Jie Xiong, Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures, Appl. Math. Optim. 30, 175-201, 1994.
    • (1994) Appl. Math. Optim , vol.30 , pp. 175-201
    • Kallianpur, Gopinath1    Xiong, Jie2
  • 23
    • 21844514446 scopus 로고
    • A class of quasilinear stochastic partial differential equation of McKean-Vlasov type with mass conservation
    • [23]
    • [23] Peter Kotelenez, A class of quasilinear stochastic partial differential equation of McKean-Vlasov type with mass conservation, Probab. Theory Relat. Fields 102, 159-188, 1995.
    • (1995) Probab. Theory Relat. Fields , vol.102 , pp. 159-188
    • Kotelenez, Peter1
  • 24
    • 0009321799 scopus 로고
    • Semigroups of conditioned shifts and approximation of Markov processes
    • [24]
    • [24] Thomas G.Kurtz, Semigroups of conditioned shifts and approximation of Markov processes,Ann. Probab. 3, 618-642, 1975.
    • (1975) Ann. Probab , vol.3 , pp. 618-642
    • Kurtz, Thomas G.1
  • 25
    • 0000817735 scopus 로고    scopus 로고
    • Weak convergence of stochastic integrals and differential equations, II. Infinite-dimensional case, Probabilistic models for nonlinear partial differential equations, 197-285
    • [25] Springer, New York
    • [25] Thomas G. Kurtz and Philip Protter, Weak convergence of stochastic integrals and differential equations, II. Infinite-dimensional case, Probabilistic models for nonlinear partial differential equations, 197-285, Lecture Notes in Math. 1-627, Springer, New York, 1996.
    • (1996) Lecture Notes in Math , pp. 1-627
    • Kurtz, Thomas G.1    Protter, Philip2
  • 26
    • 0000273833 scopus 로고    scopus 로고
    • Particle representations for a class of nonlinear SPDEs
    • [26]
    • [26] Thomas G. Kurtz and Jie Xiong, Particle representations for a class of nonlinear SPDEs, Stochastic Process Appl. 83, 103-126, 1999.
    • (1999) Stochastic Process Appl , vol.83 , pp. 103-126
    • Kurtz, Thomas G.1    Xiong, Jie2
  • 27
    • 0038772491 scopus 로고    scopus 로고
    • Numerical solutions for a class of SPDEs with application to filtering
    • [27] Edited by T. Hida, R. Karandikar, H. Kunita, B. Rajput, S. Watanabe and J. Xiong, Trends in Math. Birkhauser
    • [27] Thomas G. Kurtz and Jie Xiong, Numerical solutions for a class of SPDEs with application to filtering, Stochastics in Finite and Infinite Dimension: In Honor of Gopinath Kallianpur, Edited by T. Hida, R. Karandikar, H. Kunita, B. Rajput, S. Watanabe and J. Xiong, Trends in Math. Birkhauser, 233-258, 2000.
    • (2000) Stochastics in Finite and Infinite Dimension: In Honor of Gopinath Kallianpur , pp. 233-258
    • Kurtz, Thomas G.1    Xiong, Jie2
  • 28
    • 0002343459 scopus 로고
    • Recursive multiple Wiener integral expansion for nonlinear filtering of diffusion processes
    • [28] in Riverside, CA, Lecture Notes in Pure and Appl. Math. 186, Dekker, New York, 1997
    • [28] Sergey Lototsky and Boris L. Rozovskii, Recursive multiple Wiener integral expansion for nonlinear filtering of diffusion processes, in Stochastic Processes and Functional Analysis, Riverside, CA, 199-208, 1994, Lecture Notes in Pure and Appl. Math. 186, Dekker, New York, 1997.
    • (1994) Stochastic Processes and Functional Analysis , pp. 199-208
    • Lototsky, Sergey1    Rozovskii, Boris L.2
  • 30
    • 0003002903 scopus 로고
    • Propagation of Chaos for a Class of Non-linear Parabolic Equations
    • [30]
    • [30] Henry P. McKean, Propagation of Chaos for a Class of Non-linear Parabolic Equations,Lecture Series in Differential Equations 2, 177-194, 1967.
    • (1967) Lecture Series in Differential Equations , vol.2 , pp. 177-194
    • McKean, Henry P.1
  • 31
    • 0003311631 scopus 로고    scopus 로고
    • Asymptotic behavior of some interacting particle systems, McKean-Vlasov and Boltzmann models, Probabilistic Models for Nonlinear Partial Differential Equations
    • [31]
    • [31] Sylvie Méléard, Asymptotic behavior of some interacting particle systems, McKean-Vlasov and Boltzmann models, Probabilistic Models for Nonlinear Partial Differential Equations, Lecture Notes in Math. 1627, 42-95, 1996.
    • (1996) Lecture Notes in Math , vol.1627 , pp. 42-95
    • Méléard, Sylvie1
  • 32
    • 0000467039 scopus 로고
    • Tightness of probabilities on C([0,1],S0) and D([0,1],S0)
    • [32]
    • [32] Itaru Mitoma, Tightness of probabilities on C([0,1],S0) and D([0,1],S0), Ann. Probab. 11,989-999, 1983.
    • (1983) Ann. Probab , vol.11 , pp. 989-999
    • Mitoma, Itaru1
  • 33
    • 0001155848 scopus 로고
    • An 1-dimensional inhomogeneous Langevin's equation
    • [33]
    • [33] Itaru Mitoma, An 1-dimensional inhomogeneous Langevin's equation, J. Funct. Anal. 61,342-359, 1985.
    • (1985) J. Funct. Anal , vol.61 , pp. 342-359
    • Mitoma, Itaru1
  • 34
    • 0011028275 scopus 로고    scopus 로고
    • Propagation of chaos and fluctuations for a system of weakly interacting white noise driven parabolic SPDE's
    • [34]
    • [34] P.L. Morien, Propagation of chaos and fluctuations for a system of weakly interacting white noise driven parabolic SPDE's, Stochastics Stochastics Reps. 58, 1-43, 1996.
    • (1996) Stochastics Stochastics Reps , vol.58 , pp. 1-43
    • Morien, P.L.1
  • 35
    • 84935978811 scopus 로고
    • Approximation of nonlinear filtering problems and order of convergence, Filtering and Control of Random Processes
    • [35] Springer, New York
    • [35] J. Picard, Approximation of nonlinear filtering problems and order of convergence, Filtering and Control of Random Processes, Lecture Notes Control Inf. Sci. 61, Springer, New York, 1984.
    • (1984) Lecture Notes Control Inf. Sci , vol.61
    • Picard, J.1
  • 37
    • 0000659593 scopus 로고
    • An introduction to stochastic partial differential equations, Ecole d'été de prob-abilitées de Saint Flour
    • [37] Springer, New York
    • [37] John Walsh, An introduction to stochastic partial differential equations, Ecole d'été de prob-abilitées de Saint Flour., Lecture Notes in Math. 1180, 265-439. Springer, New York, 1984.
    • (1984) Lecture Notes in Math , vol.1180 , pp. 265-439
    • Walsh, John1


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