Strong convergence of stochastic Taylor expansions of two-parameter random fields

Stochastic Analysis and Applications

Volumn 15, Issue 2, 1997, Pages 137-149

  Anh, V V ^a   Huang, Y ^b   Kloeden, P E ^c  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^c DEAKIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040151359     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1080/07362999708809469     Document Type: Article

References (15)

1. R. Carioli and J.B. Walsh, Stochastic integrals in the plane, Acta Mathematica 134 (1975), 111-183.
2. M. Dozzi, Stochastic Processes with a Multidimensional Parameter, Longman, London, 1989.
3. B. Hajek, Stochastic equations of the hyperbolic type and a two-parameter Stratonovich calculus, Ann. Probability 10 (1982), 451-463.
4. P.E. Kloeden and E. Platen, The Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Heidelberg, 1992.
5. Yu. S, Mishura, Stochastic integrals and stochastic differential equations on the plane involving strong martingales, in New Trends in Probability and Statistics (Editors: V. Sazonov and T Sherzvashidze), 1993, pp. 485-502.
6. E. Platen and W. Wagner, On a Taylor formula for a class of Ito processes, Prob. Math. Statistics 3 (1982), 37-51.
7. J. Reid, Existence of moments of the solutions to stochastic differential equations in the plane, Ann. Probability 11 (1983), 656-668.
8. E. Wong and M. Zakai, Martingales and stochastic integrals for processes with a multidimensional parameter, Z. Wahrsch. verw. Gebiete 229 (1974), 109-122.
9. E. Wong and M. Zakai, Weak martingales and stochastic integrals in the plane, Ann. Probability 4 (1976), 570-586.
10. E. Wong and M. Zakai, An extension of stochastic integrals in the plane, Ann. Probability 5 (1977), 770-778.
11. E. Wong and M. Zakai, The sample function continuity of stochastic integrals in the plane, Ann. Probability 5 (1977), 1024-1027.
12. J. Yeh, Existence of strong solutions for stochastic differential equations in the plane, Pacific Math. J. 97 (1981), 217-247.
13. J. Yeh, Stopping times and an extension of stochastic integrals in the plane, J. Multivariate Anal. 11 (1981), 334-345.
14. J. Yeh, Existence of weak solutions for stochastic differential equations in the plane with continuous coefficients, Trans. Amer. Math. Soc. 290 (1985), 345-361.
15. V. V. Yen, A stochastic Taylor formula for functionals of two-parameter semimartingales, Acta Mathematica Vietnamica 13 (1988), 45-54.