메뉴 건너뛰기




Volumn 55, Issue 11, 2008, Pages 2413-2425

A splitting-step algorithm for reflected stochastic differential equations in R+1

Author keywords

Euler schemes; MATLAB programs; Milstein schemes; Penalization method; Reflected stochastic differential equation; Splitting step algorithm

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; EULER EQUATIONS; LINEAR EQUATIONS; NUMERICAL METHODS; STOCHASTIC MODELS;

EID: 41949137324     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.08.043     Document Type: Article
Times cited : (8)

References (23)
  • 2
    • 0008220051 scopus 로고    scopus 로고
    • Probabilistic numerical methods for partial differential equations: Elements of analysis
    • Probabilistic Models for Nonlinear Partial Differential Equations. Talay D., and Tubaro L. (Eds), Springer-Verlag, New York
    • Talay D. Probabilistic numerical methods for partial differential equations: Elements of analysis. In: Talay D., and Tubaro L. (Eds). Probabilistic Models for Nonlinear Partial Differential Equations. LNM vol. 1627 (1996), Springer-Verlag, New York 148-196
    • (1996) LNM , vol.1627 , pp. 148-196
    • Talay, D.1
  • 3
    • 0031385098 scopus 로고    scopus 로고
    • A note on probabilistic interpretation for quasilinear mixed boundary problems
    • Ding D. A note on probabilistic interpretation for quasilinear mixed boundary problems. Applied Mathematics and Mechanics 18 (1997) 857-864
    • (1997) Applied Mathematics and Mechanics , vol.18 , pp. 857-864
    • Ding, D.1
  • 5
    • 0001379748 scopus 로고
    • Stochastic equations for diffusion processes in a bounded region 1 & 2
    • 7 3-23
    • Skorokhod A.V. Stochastic equations for diffusion processes in a bounded region 1 & 2. Theory of Probability and its Applications 6 (1961) 246-274 7 3-23
    • (1961) Theory of Probability and its Applications , vol.6 , pp. 246-274
    • Skorokhod, A.V.1
  • 6
    • 0039075424 scopus 로고
    • Stochastic variational inequality for reflected diffusion
    • Menaldi J.L. Stochastic variational inequality for reflected diffusion. Indiana University Mathematics Journal 32 (1983) 733-744
    • (1983) Indiana University Mathematics Journal , vol.32 , pp. 733-744
    • Menaldi, J.L.1
  • 8
    • 0040259240 scopus 로고
    • On approximation of solutions of multidimensional SDE's with reflecting boundary conditions
    • Slominski L. On approximation of solutions of multidimensional SDE's with reflecting boundary conditions. Stochastic Processes and their Applications 50 (1994) 179-219
    • (1994) Stochastic Processes and their Applications , vol.50 , pp. 179-219
    • Slominski, L.1
  • 9
    • 41949110490 scopus 로고    scopus 로고
    • Penalization methods for reflecting stochastic differential equations with jumps
    • Laukajtys W., and Slominski L. Penalization methods for reflecting stochastic differential equations with jumps. Stochastics and Stochastics Reports 75 (2003) 275-293
    • (2003) Stochastics and Stochastics Reports , vol.75 , pp. 275-293
    • Laukajtys, W.1    Slominski, L.2
  • 10
    • 0019689061 scopus 로고
    • Strong solutions of stochastic differential equations with boundary conditions
    • Chitashvili R.J., and Lazrieva N.L. Strong solutions of stochastic differential equations with boundary conditions. Stochastics 5 (1981) 225-309
    • (1981) Stochastics , vol.5 , pp. 225-309
    • Chitashvili, R.J.1    Lazrieva, N.L.2
  • 11
    • 0000605830 scopus 로고
    • Stochastic differential equations for multi-dimensional domain with reflecting boundary
    • Saisho Y. Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probability Theory and Related Fields 74 (1987) 455-477
    • (1987) Probability Theory and Related Fields , vol.74 , pp. 455-477
    • Saisho, Y.1
  • 12
    • 0000078650 scopus 로고
    • Euler scheme for reflected stochastic differential equations
    • Lepingle D. Euler scheme for reflected stochastic differential equations. Mathematics and Computers in Simulation 38 (1995) 119-126
    • (1995) Mathematics and Computers in Simulation , vol.38 , pp. 119-126
    • Lepingle, D.1
  • 13
    • 11644285667 scopus 로고
    • Some remarks on approximation of solutions of SDE's with reflecting boundary conditions
    • Slominski L. Some remarks on approximation of solutions of SDE's with reflecting boundary conditions. Mathematics and Computers in Simulation 38 (1995) 109-117
    • (1995) Mathematics and Computers in Simulation , vol.38 , pp. 109-117
    • Slominski, L.1
  • 14
    • 41949121605 scopus 로고
    • Discretization of a class of reflected diffusion processes
    • Liu Y. Discretization of a class of reflected diffusion processes. Mathematics and Computers in Simulation 38 (1995) 103-108
    • (1995) Mathematics and Computers in Simulation , vol.38 , pp. 103-108
    • Liu, Y.1
  • 15
    • 0042044133 scopus 로고
    • Approximations for stochastic differential equations with reflecting convex boundaries
    • Pettersson R. Approximations for stochastic differential equations with reflecting convex boundaries. Stochastic Processes and their Applications 59 (1995) 295-308
    • (1995) Stochastic Processes and their Applications , vol.59 , pp. 295-308
    • Pettersson, R.1
  • 16
    • 0008119623 scopus 로고
    • Reflected diffusion processes with jumps
    • Menaldi J.L., and Robin M. Reflected diffusion processes with jumps. The Annals of Probability 13 (1985) 319-341
    • (1985) The Annals of Probability , vol.13 , pp. 319-341
    • Menaldi, J.L.1    Robin, M.2
  • 17
    • 33646367188 scopus 로고    scopus 로고
    • Approximate solution of reflecting Brownian motion using penalty method and numerical application to imperfect elastic barrier
    • Kanagawa S., Saisho Y., and Uesu H. Approximate solution of reflecting Brownian motion using penalty method and numerical application to imperfect elastic barrier. Dynamics Systems and Applications 15 2 (2005) 287-299
    • (2005) Dynamics Systems and Applications , vol.15 , Issue.2 , pp. 287-299
    • Kanagawa, S.1    Saisho, Y.2    Uesu, H.3
  • 18
    • 0042608558 scopus 로고    scopus 로고
    • Numerical analysis of SDEs without tears
    • Kannan D., and Lakshmikantham V. (Eds), Marcal Dekker, Basel
    • Schurz H. Numerical analysis of SDEs without tears. In: Kannan D., and Lakshmikantham V. (Eds). Handbook of Stochastic Analysis and Applications (2002), Marcal Dekker, Basel 27-359
    • (2002) Handbook of Stochastic Analysis and Applications , pp. 27-359
    • Schurz, H.1
  • 19
    • 41949120331 scopus 로고    scopus 로고
    • Boundary preserving semi-analytical numerical algorithms for stochastic differential equations
    • arXiv:math.NA/0509724v1 2005
    • Moro E., and Schurz H. Boundary preserving semi-analytical numerical algorithms for stochastic differential equations. SIAM Journal on Scientific Computing 29 4 (2007) 1525-1549. arXiv:math.NA/0509724v1 2005
    • (2007) SIAM Journal on Scientific Computing , vol.29 , Issue.4 , pp. 1525-1549
    • Moro, E.1    Schurz, H.2
  • 20
    • 0012279718 scopus 로고    scopus 로고
    • Strong convergence of Euler-type methods for nonlinear stochastic differential equations
    • Higham D.J., Mao X., and Stuart A.M. Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM Journal on Numerical Analysis 40 3 (2002) 1041-1061
    • (2002) SIAM Journal on Numerical Analysis , vol.40 , Issue.3 , pp. 1041-1061
    • Higham, D.J.1    Mao, X.2    Stuart, A.M.3
  • 22
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • Higham D.J. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review 43 3 (2001) 525-546
    • (2001) SIAM Review , vol.43 , Issue.3 , pp. 525-546
    • Higham, D.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.