메뉴 건너뛰기




Volumn 11, Issue , 2000, Pages 131-151

Continuous Θ-methods for the stochastic pantograph equation

Author keywords

Continuous method; Mean square convergence; Stochastic delay differential equation

Indexed keywords


EID: 3042628713     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (73)

References (30)
  • 2
    • 0034515399 scopus 로고    scopus 로고
    • Retarded differential equations
    • C. T. H. BAKER, Retarded differential equations, J. Comput. Appl. Math., 125 (2000), pp. 309-335.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 309-335
    • Baker, C.T.H.1
  • 3
    • 0012329392 scopus 로고    scopus 로고
    • Introduction to the numerical analysis of stochastic delay differential equations
    • C. T. H. BAKER AND E. BUCKWAR, Introduction to the numerical analysis of stochastic delay differential equations, LMS J. Comput. Math., 3 (2000), pp. 315-335.
    • (2000) LMS J. Comput. Math. , vol.3 , pp. 315-335
    • Baker, C.T.H.1    Buckwar, E.2
  • 4
    • 0001442051 scopus 로고
    • Issues in the numerical solution of evolutionary delay differential equations
    • C. T. H. BAKER, C. A. H. PAUL AND D. WILLÉ, Issues in the numerical solution of evolutionary delay differential equations, Adv. Comput. Math., 3 (1995), pp. 171-196.
    • (1995) Adv. Comput. Math. , vol.3 , pp. 171-196
    • Baker, C.T.H.1    Paul, C.A.H.2    Willé, D.3
  • 7
    • 84971116385 scopus 로고
    • The functional differential equation y′(x) = ay(λx) + by(x)
    • J. CARR AND J. DYSON, The functional differential equation y′(x) = ay(λx) + by(x), Proc. Roy. Soc. Edinburgh Sect. A, 74 (1974/75), pp. 165-174.
    • (1974) Proc. Roy. Soc. Edinburgh Sect. A , vol.74 , pp. 165-174
    • Carr, J.1    Dyson, J.2
  • 8
    • 0342923733 scopus 로고
    • The discretization of stochastic differential equations: A primer
    • Road Vehicle Systems and Related Mathematics; Torino, H. Neunzert, ed., Teubner, Stuttgart, and Kluwer Academic Publishers, Amsterdam
    • J. M. C. CLARK, The discretization of stochastic differential equations: a primer, in Road Vehicle Systems and Related Mathematics; Proc. 2nd DMV-GAMM Workshop, Torino, H. Neunzert, ed., Teubner, Stuttgart, and Kluwer Academic Publishers, Amsterdam, 1987, pp. 163-179.
    • (1987) Proc. 2nd DMV-GAMM Workshop , pp. 163-179
    • Clark, J.M.C.1
  • 9
    • 3042616470 scopus 로고
    • A basis for iterated stochastic integrals
    • J. G. GAINES, A basis for iterated stochastic integrals, Math. Comput. Simulation, 38 (1995), pp.7-11.
    • (1995) Math. Comput. Simulation , vol.38 , pp. 7-11
    • Gaines, J.G.1
  • 10
    • 0031258411 scopus 로고    scopus 로고
    • Variable step size control in the numerical solution of stochastic differential equations
    • J. G. GAINES AND T. L. LYONS, Variable step size control in the numerical solution of stochastic differential equations, SIAM J. Appl. Math., 57 (1997), pp. 1455-1484.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1455-1484
    • Gaines, J.G.1    Lyons, T.L.2
  • 13
    • 52649085452 scopus 로고
    • On the generalized pantograph functional-differential equation
    • A. ISERLES, On the generalized pantograph functional-differential equation, European J. Appl. Math., 4 (1993), pp. 1-38.
    • (1993) European J. Appl. Math. , vol.4 , pp. 1-38
    • Iserles, A.1
  • 15
    • 84966219417 scopus 로고
    • The functional-differential equation y′(x) = ay(λx) + by(x)
    • T. KATO AND J. B. MCLEOD, The functional-differential equation y′(x) = ay(λx) + by(x), Bull. Amer. Math. Soc., 77 (1971), pp. 891-937.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 891-937
    • Kato, T.1    Mcleod, J.B.2
  • 17
    • 0031212297 scopus 로고    scopus 로고
    • Numerical investigation of the pantograph equation
    • Y. LIU, Numerical investigation of the pantograph equation, Appl. Numer. Math., 24 (1997), pp. 309-317.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 309-317
    • Liu, Y.1
  • 18
    • 0002447873 scopus 로고
    • On stationary solutions of a stochastic differential equation
    • K. ITÔ AND M. NISIO, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ., 4 (1964), pp. 1-75.
    • (1964) J. Math. Kyoto Univ. , vol.4 , pp. 1-75
    • Itô, K.1    Nisio, M.2
  • 22
    • 0003722977 scopus 로고
    • Kluwer Academic Publishers Group, Dordrecht, translated and revised from the 1988 Russian original
    • G. N. MILSTEIN, Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers Group, Dordrecht, 1995, translated and revised from the 1988 Russian original.
    • (1995) Numerical Integration of Stochastic Differential Equations
    • Milstein, G.N.1
  • 23
    • 0021469304 scopus 로고
    • Stochastic hereditary equations: Existence and asymptotic stability
    • V. J. MIZEL AND V. TRUTZER, Stochastic hereditary equations: existence and asymptotic stability, J. Integral Equations, 7 (1984), pp. 1-72.
    • (1984) J. Integral Equations , vol.7 , pp. 1-72
    • Mizel, V.J.1    Trutzer, V.2
  • 24
    • 0010504106 scopus 로고    scopus 로고
    • Stochastic differential systems with memory. Theory, examples and applications
    • Stochastic Analysis and Related Topics VI, The Geilo Workshop, 1996, L. Decreusefond, Jon Gjerde, B. Oksendal and A.S. Ustunel, eds., Birkhauser
    • S. E. A. MOHAMMED, Stochastic differential systems with memory. Theory, examples and applications, in Stochastic Analysis and Related Topics VI, The Geilo Workshop, 1996, L. Decreusefond, Jon Gjerde, B. Oksendal and A.S. Ustunel, eds., Progress in Probability, Birkhauser, 1998, pp. 1-77.
    • (1998) Progress in Probability , pp. 1-77
    • Mohammed, S.E.A.1
  • 26
    • 0001579514 scopus 로고
    • The dynamics of a current collection system for an electric locomotive
    • J. R. OCKENDON AND A. B. TAYLER, The dynamics of a current collection system for an electric locomotive, Proc. Roy. Soc. London Ser. A, 322 (1971), pp. 447-468.
    • (1971) Proc. Roy. Soc. London Ser. A , vol.322 , pp. 447-468
    • Ockendon, J.R.1    Tayler, A.B.2
  • 27
    • 85011454437 scopus 로고    scopus 로고
    • An introduction to numerical methods for stochastic differential equations
    • E. PLATEN, An introduction to numerical methods for stochastic differential equations, Acta Numerica, 8 (1999), pp. 195-244.
    • (1999) Acta Numerica , vol.8 , pp. 195-244
    • Platen, E.1
  • 28
    • 0003208202 scopus 로고
    • Simulation of stochastic differential systems
    • Probabilistic Methods in Applied Physics, P. Krée and W. Wedig, eds., Springer, Berlin
    • D. TAL AY, Simulation of stochastic differential systems, in Probabilistic Methods in Applied Physics, P. Krée and W. Wedig, eds., Lecture Notes in Physics 451, Springer, Berlin, 1995, pp. 54-96.
    • (1995) Lecture Notes in Physics , vol.451 , pp. 54-96
    • Tal Ay, D.1
  • 30
    • 0000446512 scopus 로고
    • Delay differential equations: Theory and numerics
    • M. Ainsworth, J. Levesley, W. A. Light and M. Marletta, eds., Oxford University Press, New York
    • M. ZENNARO, Delay differential equations: theory and numerics, in Theory and Numerics of Ordinary and Partial Differential Equations, M. Ainsworth, J. Levesley, W. A. Light and M. Marletta, eds., Oxford University Press, New York, 1995, pp. 291-333.
    • (1995) Theory and Numerics of Ordinary and Partial Differential Equations , pp. 291-333
    • Zennaro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.