Stochastic Taylor expansions for functionals of diffusion processes

Stochastic Analysis and Applications

Volumn 28, Issue 3, 2010, Pages 415-429

  Rößler, Andreas ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Mean square approximation; Multi colored rooted tree analysis; Stochastic differential equation; Stochastic Taylor expansion; Strong approximation

Indexed keywords

EID: 77951187649     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362991003707905     Document Type: Article

References (12)

1. Arnold, L. 1974. Stochastic Differential Equations, John Wiley & Sons, New York.
2. Burrage, K., and Burrage, P.M. 2000. Order conditions of stochastic Runge-Kutta methods by B-series. SIAM Journal of Numerical Analysis 38:1626-1646.
3. Butcher, J.C. 2003. Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, Chichester, UK.
4. Karatzas, I., and Shreve, S.E. 1999. Brownian Motion and Stochastic Calculus, Springer, New York.
5. Kloeden, P.E., and Platen, E. 1999. Numerical Solution of Stochastic Differential Equations, Applications of Mathematics 23, Springer-Verlag, Berlin.
6. Milstein, G.N. 1995. Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers, Dordrecht.
7. Milstein, G.N., and Tretyakov, M.V. 2004. Stochastic Numerics for Mathematical Physics, Springer-Verlag, Berlin.
8. Neuenkirch, A., Nourdin, I., Rößler, A., and Tindel, S. 2009. Trees and asymptotic expansions for fractional stochastic differential equations. Annals of the Institute Henri Poincaré Probability Statistics 45:157-174.
9. Øksendal, B. 1998. Stochastic Differential Equations, Applications of Mathematics 21, Springer-Verlag, Berlin.
10. Platen, E., and Wagner, W. 1982. On a Taylor formula for a class of Itô processes. Probabilities in Mathematics and Statistics 3:37-51.
11. Rößler, A. 2006. Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations. Stochastic Analysis and Applications 24:97-134.
12. Rößler, A. 2004. Stochastic Taylor expansions for the expectation of functionals of diffusion processes. Stochastic Analysis and Applications 22:1553-1576.