Strong approximation of reflecting brownian motion using penalty method and its application to cumputer simulation

Monte Carlo Methods and Applications

Volumn 6, Issue 2, 2000, Pages 105-114

  Kanagawa, S ^a   Saisho, Y ^b  

^a KANAZAWA UNIVERSITY   (Japan)

^b KUMAMOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10244230650     PISSN: 09299629     EISSN: 15693961     Source Type: Journal    
DOI: 10.1515/mcma.2000.6.2.105     Document Type: Article

References (18)

1. S. Kanagawa, On the rate of convergence for Maruyama's approximate Solutions of stochastic differential equations, Yokohama Mathematical Journal 36 (1988) 79-86.
2. D. Lepingle, Un Schema d'Euler pour equations difFerentielles stochaistiques feflechies, C.R.Acad.Sci.Paris I 316 (1993) 601-605.
3. O.Faure, Numerical pathwise approximation of stochastic differential equations, Prepublication of LAMM, Ecole Nationale des Fonts et Chaussees, Paris (1990)
4. P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. XXXVII (1981) 511-537.
5. Y. Liu, Numerical approaches to reflected diffusion processes, Manuscript, Department of Mathematics, Purdue University, Indiana (1993).
6. G. Maruyama, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo 4 (1955) 48-90.
7. J.L. Menaldi, Stochastic variational inequality for reflecting diffusion, Indiana Univ. Math. Jour. 32 (1983) 733-744.
8. J.L. Menaldi and M. Robin, Reflected diffusion processes with Jumps, Ann. Probab. 13 (1985) 319-341.
9. R. Pettersson, Approximation for stochastic differential equations with reflecting convex boundaries, Stoch. Processes Appl. 59 (1995) 295-308.
10. R. Pettersson, Penalization schemes for reflecting stochastic differential equations, to appear in Stoch. Processes Appl.
11. R. Pettersson, Projection scheme for stochastic differential equations with convex constants, preprint.
12. Y.Saisho, Multi-dimensional Skorohod equations and reflecting diffusions, A dissertation submitted to Keio University (1986).
13. Y. Saisho, Stochastic differential equations for multi-dimensional domain with reflecting boundary, Probab. Theory Rel. Fields 74 (1987) 455-477.
14. Y. Saisho and H. Tanaka, Stochastic differential equations for mutually reflecting Brownian balls, Osaka J. Math. 23 (1986), 725-740.
15. Y. Saisho and H. Tanaka, On the symmetry of a reflecting Brownian motion defined by Skorohod's equation for a multi-dimensional domain, Tokyo J.Math. 10 (1987), 419-435.
16. L. Slominski, On existence, uniqueness and stability of Solutions of multidimensional SDE's with reflecting boundary conditions, Ann. Inst. H. Poincare 29 (1993) 163-198.
17. L. Slominski, On approximation of Solutions of multidimensional SDE's with reflecting boundary conditions, Stoch. Processes Appl. 50 (1994) 197-219.
18. H. Tanaka, Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J. 9 (1979) 163-177.