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Volumn 32, Issue 1 A, 2004, Pages 265-314

Discrete-time approximations of stochastic delay equations: The milstein scheme

Author keywords

Anticipating calculus; Ito circ; 's formula; Malliavin calculus; Milstein scheme; Tame functions; Weak derivatives

Indexed keywords


EID: 2142818234     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1078415836     Document Type: Article
Times cited : (104)

References (29)
  • 2
    • 0043136587 scopus 로고    scopus 로고
    • An extension of Itoˆ's formula for anticipating processes
    • ALÒS, E. and NUALART, D. (1998). An extension of Itoˆ's formula for anticipating processes. J. Theoret. Probab. 2 493-514.
    • (1998) J. Theoret. Probab. , vol.2 , pp. 493-514
    • Alòs, E.1    Nualart, D.2
  • 3
    • 0002217809 scopus 로고
    • Itoˆ's lemma without non-anticipatory conditions
    • ASCH, J. and POTTHOFF, J. (1991). Itoˆ's lemma without non-anticipatory conditions. Probab. Theory Related Fields 88 17-46.
    • (1991) Probab. Theory Related Fields , vol.88 , pp. 17-46
    • Asch, J.1    Potthoff, J.2
  • 4
    • 0012329392 scopus 로고    scopus 로고
    • Numerical analysis of explicit one-step methods for stochastic delay differential equations
    • electronic
    • BAKER, C. T. H. and BUCKWAR, E. (2000). Numerical analysis of explicit one-step methods for stochastic delay differential equations. LMS J. Comput. Math. 3 315-335 (electronic). Available at www.lms.ac.uk/jcm.
    • (2000) LMS J. Comput. Math. , vol.3 , pp. 315-335
    • Baker, C.T.H.1    Buckwar, E.2
  • 5
    • 0007348750 scopus 로고
    • On the solution of stochastic ordinary differential equations via small delays
    • BELL, D. and MOHAMMED, S.-E. A. (1989). On the solution of stochastic ordinary differential equations via small delays. Stochastics Stochastics Rep. 28 293- 299.
    • (1989) Stochastics Stochastics Rep. , vol.28 , pp. 293-299
    • Bell, D.1    Mohammed, S.-E.A.2
  • 6
    • 0042887856 scopus 로고
    • The Malliavin calculus and stochastic delay equations
    • BELL, D. and MOHAMMED, S.-E. A. (1991). The Malliavin calculus and stochastic delay equations. J. Funct. Anal. 99 75-99.
    • (1991) J. Funct. Anal. , vol.99 , pp. 75-99
    • Bell, D.1    Mohammed, S.-E.A.2
  • 7
    • 0010779278 scopus 로고
    • An extension of the stochastic integral
    • BERGER, M. and MIZEL, V. J. (1982). An extension of the stochastic integral. Ann. Probab. 10 435-450.
    • (1982) Ann. Probab. , vol.10 , pp. 435-450
    • Berger, M.1    Mizel, V.J.2
  • 8
    • 0007470214 scopus 로고    scopus 로고
    • The exact convergence rate of Euler-Maruyama scheme and application to sample design
    • CAMBANIS, S. and Hu, Y. (1996). The exact convergence rate of Euler-Maruyama scheme and application to sample design. Stochastics Stochastics Rep. 59 211-240.
    • (1996) Stochastics Stochastics Rep. , vol.59 , pp. 211-240
    • Cambanis, S.1    Hu, Y.2
  • 9
    • 2142705156 scopus 로고
    • The Hu-Meyer formula for non-deterministic kernels
    • DELGADO, R. and SANZ, M. (1992). The Hu-Meyer formula for non-deterministic kernels. Stochastics Stochastics Rep. 38 149-158.
    • (1992) Stochastics Stochastics Rep. , vol.38 , pp. 149-158
    • Delgado, R.1    Sanz, M.2
  • 11
    • 0028485279 scopus 로고
    • Random generation of stochastic area integrals
    • GAINES, J. G. and LYONS, T. J. (1994). Random generation of stochastic area integrals. SIAM J. Appl. Math. 54 1132-1146.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1132-1146
    • Gaines, J.G.1    Lyons, T.J.2
  • 13
    • 0040743280 scopus 로고    scopus 로고
    • Strong and weak order of time discretization schemes of stochastic differential equations
    • Springer, Berlin
    • Hu, Y. (1996). Strong and weak order of time discretization schemes of stochastic differential equations. Se´minaire de Probabilite´s XXX. Lecture Notes in Math. 1626 218-227. Springer, Berlin.
    • (1996) Se´minaire de Probabilite´s XXX. Lecture Notes in Math. , vol.1626 , pp. 218-227
    • Hu, Y.1
  • 14
    • 2142816598 scopus 로고    scopus 로고
    • Optimal times to observe in the Kalman-Bucy model
    • Hu, Y. (2000). Optimal times to observe in the Kalman-Bucy model. Stochastics Stochastic Rep. 69 123-140.
    • (2000) Stochastics Stochastic Rep. , vol.69 , pp. 123-140
    • Hu, Y.1
  • 16
    • 0010027221 scopus 로고
    • On generalized multiple stochastic integrals and multiparameter anticipative calculus
    • Springer, New York
    • JOLIS, M. and SANZ, M. (1988). On generalized multiple stochastic integrals and multiparameter anticipative calculus, Stochastic Analysis and Related Topics II. Lecture Notes in Math. 1444 141-182. Springer, New York.
    • (1988) Stochastic Analysis and Related Topics II. Lecture Notes in Math. , vol.1444 , pp. 141-182
    • Jolis, M.1    Sanz, M.2
  • 21
    • 0010504106 scopus 로고    scopus 로고
    • Stochastic differential systems with memory: Theory, examples and applications
    • (L. Decreusefond, J. Gjerde, B. Øksendal and A. S. Ustunel, eds.). Birkha¨user, Boston
    • MOHAMMED, S.-E. A. (1998). Stochastic differential systems with memory: Theory, examples and applications. In Stochastic Analysis and Related Topics VI (L. Decreusefond, J. Gjerde, B. Øksendal and A. S. Ustunel, eds.) 1-77. Birkha¨user, Boston.
    • (1998) Stochastic Analysis and Related Topics VI , pp. 1-77
    • Mohammed, S.-E.A.1
  • 23
    • 0001626619 scopus 로고
    • Stochastic calculus with anticipating integrands
    • NUALART, D. and PARDOUX, E. (1988). Stochastic calculus with anticipating integrands. Probab. Theory Related Fields 78 535-581.
    • (1988) Probab. Theory Related Fields , vol.78 , pp. 535-581
    • Nualart, D.1    Pardoux, E.2
  • 24
    • 0000084472 scopus 로고
    • Stochastic Volterra equations with anticipating coefficients
    • PARDOUX, E. and PROTTER, P. (1990). Stochastic Volterra equations with anticipating coefficients. Ann. Probab. 18 1635-1655.
    • (1990) Ann. Probab. , vol.18 , pp. 1635-1655
    • Pardoux, E.1    Protter, P.2
  • 25
    • 21344479524 scopus 로고
    • Forward, backward and symmetric stochastic integration
    • RUSSO, F. and VALLOIS, P. (1993). Forward, backward and symmetric stochastic integration. Probab. Theory Related Fields 97 403-421.
    • (1993) Probab. Theory Related Fields , vol.97 , pp. 403-421
    • Russo, F.1    Vallois, P.2
  • 26
    • 0007336796 scopus 로고    scopus 로고
    • On the simulation of iterated Itoˆ integrals
    • RYDEN, T. and WIKTORSSON, M. (2001). On the simulation of iterated Itoˆ integrals. Stochastic Process. Appl. 91 151-168.
    • (2001) Stochastic Process. Appl. , vol.91 , pp. 151-168
    • Ryden, T.1    Wiktorsson, M.2
  • 28
    • 2142643132 scopus 로고    scopus 로고
    • Ph.D. dissertation, Southern Illinois Univ., Carbondale, Illinois
    • YAN, F. (1999). Topics on stochastic delay equations. Ph.D. dissertation, Southern Illinois Univ., Carbondale, Illinois.
    • (1999) Topics on Stochastic Delay Equations
    • Yan, F.1
  • 29
    • 0039644587 scopus 로고
    • Stochastic integration, trace and the skeleton of Wiener functionals
    • ZAKAI, M. (1990). Stochastic integration, trace and the skeleton of Wiener functionals. Stochastics Stochastics Rep. 32 93-108.
    • (1990) Stochastics Stochastics Rep. , vol.32 , pp. 93-108
    • Zakai, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.