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Volumn 5, Issue , 2001, Pages 261-297

Euler schemes and half–space approximation for the simulation of diffusion in a domain

Author keywords

Boundary value problems for parabolic PDE; Discretization schemes; Killed diffusion; Rates of convergence; Reflected diffusion; Weak approximation

Indexed keywords


EID: 84996131097     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps:2001112     Document Type: Article
Times cited : (84)

References (34)
  • 1
    • 21344452934 scopus 로고
    • Exact asymptotics for the probability of exit from a domain and applications to simulation
    • P. Baldi, Exact asymptotics for the probability of exit from a domain and applications to simulation. Ann. Probab. 23 (1995) 1644-1670.
    • (1995) Ann. Probab. , vol.23 , pp. 1644-1670
    • Baldi, P.1
  • 2
    • 65249176273 scopus 로고    scopus 로고
    • Pricing complex barrier options with general features using sharp large deviation estimates
    • edited by Niederreiter, Harald et al., Monte-Carlo and quasi-Monte-Carlo methods 1998. Claremont, CA, USA, June 22-26, Springer, Berlin
    • P. Baldi, L. Caramellino and M.G. Iovino, Pricing complex barrier options with general features using sharp large deviation estimates, edited by Niederreiter, Harald et al., Monte-Carlo and quasi-Monte-Carlo methods 1998, in Proc. of a conference held at the Claremont Graduate University. Claremont, CA, USA, June 22-26, 1998. Springer, Berlin (2000) 149-162.
    • (2000) Proc. Of a Conference Held at the Claremont Graduate University , vol.1998 , pp. 149-162
    • Baldi, P.1    Caramellino, L.2    Iovino, M.G.3
  • 3
    • 0030560429 scopus 로고    scopus 로고
    • The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function
    • V. Bally and D. Talay, The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function. Probab. Theory Related Fields 104-1 (1996) 43-60.
    • (1996) Probab. Theory Related Fields , vol.104 , Issue.1 , pp. 43-60
    • Bally, V.1    Talay, D.2
  • 5
    • 0013298667 scopus 로고
    • Hypoellipticite et hypoellipticite partielle pour les diffusions avec une condition frontiere
    • P. Cattiaux, Hypoellipticite et hypoellipticite partielle pour les diffusions avec une condition frontiere. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986) 67-112.
    • (1986) Ann. Inst. H. Poincaré Probab. Statist. , vol.22 , pp. 67-112
    • Cattiaux, P.1
  • 6
    • 0013249402 scopus 로고
    • Regularite au bord pour les densites et les densites conditionnelles d’une diffusion reflechie hypoelliptique
    • P. Cattiaux, Regularite au bord pour les densites et les densites conditionnelles d’une diffusion reflechie hypoelliptique. Stochastics 20 (1987) 309-340.
    • (1987) Stochastics , vol.20 , pp. 309-340
    • Cattiaux, P.1
  • 7
    • 0031997542 scopus 로고    scopus 로고
    • Numerical approximation for functionnals of reflecting diffusion processes
    • C. Constantini, B. Pacchiarotti and F. Sartoretto, Numerical approximation for functionnals of reflecting diffusion processes. SIAM J. Appl. Math. 58 (1998) 73-102.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 73-102
    • Constantini, C.1    Pacchiarotti, B.2    Sartoretto, F.3
  • 9
    • 0003200789 scopus 로고
    • Functional integration and partial differential equations
    • Princeton University Press
    • M. Freidlin, Functional integration and partial differential equations. Ann. of Math. Stud. Princeton University Press (1985).
    • (1985) Ann. Of Math. Stud
    • Freidlin, M.1
  • 12
    • 0012074125 scopus 로고    scopus 로고
    • Euler schemes for the weak approximation of killed diffusion
    • E. Gobet, Euler schemes for the weak approximation of killed diffusion. Stochastic Process. Appl. 87 (2000) 167-197.
    • (2000) Stochastic Process. Appl. , vol.87 , pp. 167-197
    • Gobet, E.1
  • 13
    • 10244226450 scopus 로고    scopus 로고
    • Efficient schemes for the weak approximation of reflected diffusions
    • E. Gobet, Efficient schemes for the weak approximation of reflected diffusions. Monte Carlo Methods Appl. 7 (2001) 193-202.
    • (2001) Monte Carlo Methods Appl , vol.7 , pp. 193-202
    • Gobet, E.1
  • 15
    • 77951921851 scopus 로고    scopus 로고
    • A numerical scheme using excursion theory for simulating stochastic differential equations with reflection and local time at a boundary
    • E. Hausenblas, A numerical scheme using excursion theory for simulating stochastic differential equations with reflection and local time at a boundary. Monte Carlo Methods Appl. 6 (2000) 81-103.
    • (2000) Monte Carlo Methods Appl , vol.6 , pp. 81-103
    • Hausenblas, E.1
  • 16
    • 10244230650 scopus 로고    scopus 로고
    • Strong approximation of reflecting Brownian motion using penalty method and its application to computer simulation
    • S. Kanagawa and Y. Saisho, Strong approximation of reflecting Brownian motion using penalty method and its application to computer simulation. Monte Carlo Methods Appl. 6 (2000) 105-114.
    • (2000) Monte Carlo Methods Appl , vol.6 , pp. 105-114
    • Kanagawa, S.1    Saisho, Y.2
  • 17
    • 77956845256 scopus 로고
    • Applications of the Malliavin calculus I, edited by K. Itô, Stochastic Analysis
    • Kinokuniya, Tokyo
    • S. Kusuoka and D. Stroock, Applications of the Malliavin calculus I, edited by K. Itô, Stochastic Analysis, in Proc. Taniguchi Internatl. Symp. Katata and Kyoto 1982. Kinokuniya, Tokyo (1984) 271-306.
    • (1984) Proc. Taniguchi Internatl. Symp. Katata and Kyoto , vol.1982 , pp. 271-306
    • Kusuoka, S.1    Stroock, D.2
  • 19
    • 0042044299 scopus 로고
    • Un schema d’Euler pour équations différentielles stochastiques reflechies
    • D. Lepingle, Un schema d’Euler pour équations différentielles stochastiques reflechies. C. R. Acad. Sci. Paris Sér. I Math. 316 (1993) 601-605.
    • (1993) C. R. Acad. Sci. Paris Sér. I Math. , vol.316 , pp. 601-605
    • Lepingle, D.1
  • 20
    • 0000078650 scopus 로고
    • Euler scheme for reflected stochastic differential equations
    • D. Lepingle, Euler scheme for reflected stochastic differential equations. Math. Comput. Simulation 38 (1995) 119-126.
    • (1995) Math. Comput. Simulation , vol.38 , pp. 119-126
    • Lepingle, D.1
  • 21
    • 84990576543 scopus 로고
    • Stochastic differential equations with reflecting boundary conditions
    • P. L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984) 511-537.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 511-537
    • Lions, P.L.1    Sznitman, A.S.2
  • 23
    • 0039075424 scopus 로고
    • Stochastic variational inequality for reflected diffusion
    • J.L. Menaldi, Stochastic variational inequality for reflected diffusion. Indiana Univ. Math. J. 32 (1983) 733-744.
    • (1983) Indiana Univ. Math. J. , vol.32 , pp. 733-744
    • Menaldi, J.L.1
  • 24
    • 0030344091 scopus 로고    scopus 로고
    • Application of the numerical integration of stochastic equations for the solution of boundary value problems with Neumann boundary conditions
    • G.N. Milshtein, Application of the numerical integration of stochastic equations for the solution of boundary value problems with Neumann boundary conditions. Theory Probab. Appl. 41 (1996) 170-177.
    • (1996) Theory Probab. Appl. , vol.41 , pp. 170-177
    • Milshtein, G.N.1
  • 27
    • 0042044133 scopus 로고
    • Approximations for stochastic differential equations with reflecting convex boundaries
    • R. Pettersson, Approximations for stochastic differential equations with reflecting convex boundaries. Stochastic Process. Appl. 59 (1995) 295-308.
    • (1995) Stochastic Process. Appl. , vol.59 , pp. 295-308
    • Pettersson, R.1
  • 28
    • 0041568068 scopus 로고    scopus 로고
    • Penalization schemes for reflecting stochastic differential equations
    • R. Pettersson, Penalization schemes for reflecting stochastic differential equations. Bernoulli 3 (1997) 403-414.
    • (1997) Bernoulli , vol.3 , pp. 403-414
    • Pettersson, R.1
  • 29
    • 0344939351 scopus 로고
    • Continuous martingales and Brownian motion
    • 2nd Ed. Springer, Berlin
    • D. Revuz and M. Yor, Continuous martingales and Brownian motion, 2nd Ed. Springer, Berlin, Grundlehren Math. Wiss. 293 (1994).
    • (1994) Grundlehren Math. Wiss , vol.293
    • Revuz, D.1    Yor, M.2
  • 30
    • 0000605830 scopus 로고
    • Stochastic differential equations for multi-dimensional domain with reflecting boundary
    • Y. Saisho, Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probab. Theory Related Fields 74 (1987) 455-477.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 455-477
    • Saisho, Y.1
  • 31
    • 0001358269 scopus 로고
    • The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables
    • J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Philos. Trans. Roy. Soc. London Ser. A 264 (1969) 413-496.
    • (1969) Philos. Trans. Roy. Soc. London Ser. A , vol.264 , pp. 413-496
    • Serrin, J.1
  • 32
    • 0040259240 scopus 로고
    • On approximation of solutions of multidimensional SDEs with reflecting boundary conditions
    • L. Slominski, On approximation of solutions of multidimensional SDEs with reflecting boundary conditions. Stochastic Process. Appl. 50 (1994) 197-219.
    • (1994) Stochastic Process. Appl. , vol.50 , pp. 197-219
    • Slominski, L.1
  • 33
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving stochastic differential equations
    • D. Talay and L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Aral. Appl. 8-4 (1990) 94-120.
    • (1990) Stochastic Aral. Appl. , vol.8-4 , pp. 94-120
    • Talay, D.1    Tubaro, L.2


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