메뉴 건너뛰기




Volumn 41, Issue 1, 2009, Pages 63-100

Monte Carlo methods for backward equations in nonlinear filtering

Author keywords

Kallianpur Striebel formula; Mean square and weak numerical methods; Monte Carlo technique; Pathwise filtering equation; Stochastic partial differential quation

Indexed keywords

KALLIANPUR-STRIEBEL FORMULA; MEAN-SQUARE AND WEAK NUMERICAL METHODS; MONTE CARLO TECHNIQUE; PATHWISE FILTERING EQUATION; STOCHASTIC PARTIAL DIFFERENTIAL QUATION;

EID: 67649657680     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1240319577     Document Type: Article
Times cited : (9)

References (28)
  • 1
    • 0019660565 scopus 로고    scopus 로고
    • BENEŠ, V.E. (1981). Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics 5, 65-92.
    • BENEŠ, V.E. (1981). Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics 5, 65-92.
  • 3
    • 67649637239 scopus 로고    scopus 로고
    • CLARK, J.M.C. (1978). The design of robust approximations to the stochastic differential equations of nonlinear filtering. In Communication Systems and Random Process Theory (Proc. 2nd NATO Adv. Study Inst., Darlington, 1977) ed. J.K. Skwirzynski, Sijthoff and Noordhoff, pp. 721-734.
    • CLARK, J.M.C. (1978). The design of robust approximations to the stochastic differential equations of nonlinear filtering. In Communication Systems and Random Process Theory (Proc. 2nd NATO Adv. Study Inst., Darlington, 1977) ed. J.K. Skwirzynski, Sijthoff and Noordhoff, pp. 721-734.
  • 4
    • 0038336146 scopus 로고    scopus 로고
    • Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation
    • CRISAN, D. (2003). Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation. Ann. Prob. 31, 693-718.
    • (2003) Ann. Prob , vol.31 , pp. 693-718
    • CRISAN, D.1
  • 5
    • 0033261066 scopus 로고    scopus 로고
    • A particle approximation of the solution of the Kushner-Stratonovich equation
    • CRISAN, D. AND LYONS, T. (1999). A particle approximation of the solution of the Kushner-Stratonovich equation. Prob. Theory Relat. Fields 115, 549-578.
    • (1999) Prob. Theory Relat. Fields , vol.115 , pp. 549-578
    • CRISAN, D.1    LYONS, T.2
  • 6
    • 0019610091 scopus 로고    scopus 로고
    • DAVIS, M.H.A. (1981). New approach for filtering for nonlinear systems. Institution IEE Proc. D 128, 166-172.
    • DAVIS, M.H.A. (1981). New approach for filtering for nonlinear systems. Institution IEE Proc. D 128, 166-172.
  • 7
    • 67649653709 scopus 로고    scopus 로고
    • DAVIS, M.H.A. (1981). Pathwise nonlinear filtering. In Stochastic Systems: The Mathematics of Filtering and Identification and Applications (Proc. NATO Adv. Study Inst., Les Arcs, 1980), eds M. Hazewinkel and J.C. Willems, Reidel, Dordrecht, pp. 505-528.
    • DAVIS, M.H.A. (1981). Pathwise nonlinear filtering. In Stochastic Systems: The Mathematics of Filtering and Identification and Applications (Proc. NATO Adv. Study Inst., Les Arcs, 1980), eds M. Hazewinkel and J.C. Willems, Reidel, Dordrecht, pp. 505-528.
  • 8
    • 67649653708 scopus 로고    scopus 로고
    • DAVIS, M.H.A. (1982). A pathwise solution of the equations of nonlinear filtering. Theory Prob. Appl. 27, 160-167.
    • DAVIS, M.H.A. (1982). A pathwise solution of the equations of nonlinear filtering. Theory Prob. Appl. 27, 160-167.
  • 9
    • 0001534675 scopus 로고    scopus 로고
    • Nonlinear filtering: Interacting particle solution
    • DEL MORAL, P. (1996). Nonlinear filtering: interacting particle solution. Markov Process. Relat. Fields 2, 555-579.
    • (1996) Markov Process. Relat. Fields , vol.2 , pp. 555-579
    • DEL MORAL, P.1
  • 10
    • 0002936641 scopus 로고    scopus 로고
    • Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering
    • Séminaire de Probabilités XXXIV, Springer, Berlin, pp
    • DEL MORAL, P. AND MICLO, L. (2000). Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. In Séminaire de Probabilités XXXIV (Lecture Notes in Math. 1729), Springer, Berlin, pp. 1-145.
    • (2000) Lecture Notes in Math , vol.1729 , pp. 1-145
    • DEL MORAL, P.1    MICLO, L.2
  • 11
    • 67649661773 scopus 로고    scopus 로고
    • DYNKIN, E.B. (1965). Markov Processes. Springer, New York.
    • DYNKIN, E.B. (1965). Markov Processes. Springer, New York.
  • 12
    • 0000889320 scopus 로고    scopus 로고
    • Approximation of the Kushner equation for nonlinear filtering
    • ITÔ, K. AND ROZOVSKII, B. (2000). Approximation of the Kushner equation for nonlinear filtering. SIAM J. Control Optimization 38, 893-915.
    • (2000) SIAM J. Control Optimization , vol.38 , pp. 893-915
    • ITÔ, K.1    ROZOVSKII, B.2
  • 13
    • 0038772491 scopus 로고    scopus 로고
    • Numerical solutions for a class of SPDEs with application to filtering
    • Birkhäuser, Boston, pp
    • KURTZ, T.G. AND XIONG, J. (2001). Numerical solutions for a class of SPDEs with application to filtering. In Stochastics in Finite and Infinite Dimensions, Birkhäuser, Boston, pp. 233-258.
    • (2001) Stochastics in Finite and Infinite Dimensions , pp. 233-258
    • KURTZ, T.G.1    XIONG, J.2
  • 14
    • 67649641388 scopus 로고    scopus 로고
    • KUSHNER, H.J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. Academic Press, New York.
    • KUSHNER, H.J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. Academic Press, New York.
  • 15
    • 0042044191 scopus 로고
    • Splitting-up approximation for SPDEs and SDEs with application to nonlinear filtering
    • Stochastic Partial Differential Equations and Their Applications, Springer, Berlin, pp
    • LE GLAND, F. (1992). Splitting-up approximation for SPDEs and SDEs with application to nonlinear filtering. In Stochastic Partial Differential Equations and Their Applications (Lecture Notes Control and Inform. Sci. 176), Springer, Berlin, pp. 177-187.
    • (1992) Lecture Notes Control and Inform. Sci , vol.176 , pp. 177-187
    • LE GLAND, F.1
  • 17
    • 2942623146 scopus 로고    scopus 로고
    • Numerical construction of a hedging strategy against the multi-asset European claim
    • Stoch. Stoch
    • MILSTEIN, G.N. AND SCHOENMAKERS, J.G.M. (2002). Numerical construction of a hedging strategy against the multi-asset European claim. Stoch. Stoch. Reports 73, 125-157.
    • (2002) Reports , vol.73 , pp. 125-157
    • MILSTEIN, G.N.1    SCHOENMAKERS, J.G.M.2
  • 19
    • 67649637238 scopus 로고    scopus 로고
    • Averaging over characteristics with innovation approach in nonlinear filtering
    • eds D. Crisan and B. Rozovskii, Oxford University Press to appear
    • MILSTEIN, G.N. AND TRETYAKOV, M.V. (2009). Averaging over characteristics with innovation approach in nonlinear filtering. In Handbook on Nonlinear Filtering, eds D. Crisan and B. Rozovskii, Oxford University Press (to appear).
    • (2009) Handbook on Nonlinear Filtering
    • MILSTEIN, G.N.1    TRETYAKOV, M.V.2
  • 20
    • 67649644310 scopus 로고    scopus 로고
    • Solving parabolic stochastic partial differential equations via averaging over characteristics
    • To appear in
    • MILSTEIN, G.N. AND TRETYAKOV, M.V. (2009). Solving parabolic stochastic partial differential equations via averaging over characteristics. To appear in Math. Comput.
    • (2009) Math. Comput
    • MILSTEIN, G.N.1    TRETYAKOV, M.V.2
  • 21
    • 33644476835 scopus 로고    scopus 로고
    • Transition density estimation for stochastic differential equations via forward-reverse representations
    • MILSTEIN, G.N., SCHOENMAKERS, J.G.M. AND SPOKOINY, V. (2004). Transition density estimation for stochastic differential equations via forward-reverse representations. Bernoulli 10, 281-312.
    • (2004) Bernoulli , vol.10 , pp. 281-312
    • MILSTEIN, G.N.1    SCHOENMAKERS, J.G.M.2    SPOKOINY, V.3
  • 22
    • 0041707111 scopus 로고    scopus 로고
    • NEWTON, N.J. (2000). Observation sampling and quantisation for continuous-time estimators. Stoch. Process. Appl. 87, 311-337.
    • NEWTON, N.J. (2000). Observation sampling and quantisation for continuous-time estimators. Stoch. Process. Appl. 87, 311-337.
  • 23
    • 67649637234 scopus 로고    scopus 로고
    • PARDOUX, E. (1981). Nonlinear filtering, prediction and smoothing. In Stochastic Systems: The Mathematics of Filtering and Identification and Applications (NATO Adv. Study Inst., Les Arcs, 1980), eds M. Hazewinkel and J.C. Willems, Reidel, Dordrecht, pp. 529-557.
    • PARDOUX, E. (1981). Nonlinear filtering, prediction and smoothing. In Stochastic Systems: The Mathematics of Filtering and Identification and Applications (NATO Adv. Study Inst., Les Arcs, 1980), eds M. Hazewinkel and J.C. Willems, Reidel, Dordrecht, pp. 529-557.
  • 24
    • 0020013917 scopus 로고
    • Équations du filtrage nonlinéaire, de la prédiction et du lissage.
    • PARDOUX, E. (1982). Équations du filtrage nonlinéaire, de la prédiction et du lissage. Stochastics 6, 193-231.
    • (1982) Stochastics , vol.6 , pp. 193-231
    • PARDOUX, E.1
  • 25
    • 0021293613 scopus 로고
    • Approximation of nonlinear filtering problems and order of convergence
    • Filtering and Control of Random Processes, Springer, Berlin, pp
    • PICARD, J. (1984). Approximation of nonlinear filtering problems and order of convergence. In Filtering and Control of Random Processes (Lecture Notes Control Inform. Sci. 61), Springer, Berlin, pp. 219-236.
    • (1984) Lecture Notes Control Inform. Sci , vol.61 , pp. 219-236
    • PICARD, J.1
  • 26
    • 67649649539 scopus 로고    scopus 로고
    • ROZOVSKII, B.L. (1990). Stochastic Evolution Systems. Kluwer, Dordrecht.
    • ROZOVSKII, B.L. (1990). Stochastic Evolution Systems. Kluwer, Dordrecht.
  • 27
    • 0021313777 scopus 로고
    • Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications
    • Filtering and Control of Random Processes, Springer, Berlin, pp
    • TALAY, D. (1984). Efficient numerical schemes for the approximation of expectations of functionals of the solution of a SDE and applications. In Filtering and Control of Random Processes (Lecture Notes Control Inform. Sci. 61), Springer, Berlin, pp. 294-313.
    • (1984) Lecture Notes Control Inform. Sci , vol.61 , pp. 294-313
    • TALAY, D.1
  • 28
    • 0004394334 scopus 로고
    • Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution.
    • TALAY, D. (1986). Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution. RAIRO Modél. Math. Anal. Numér. 20, 141-179.
    • (1986) RAIRO Modél. Math. Anal. Numér , vol.20 , pp. 141-179
    • TALAY, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.