Approximation of feller processes by Markov Chains with Lévy increments

Stochastics and Dynamics

Volumn 9, Issue 1, 2009, Pages 71-80

  Böttcher, Björn ^a   Schilling, René L ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Euler scheme; Feller process; Jump process; Markov chain approximation; Pseudo differential operator

Indexed keywords

EID: 65449170021     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493709002555     Document Type: Article

References (22)

1. R. F. Bass, Uniqueness in law for pure jump type Markov processes, Probab. Th. Relat. Fields 79 (1988) 271-287.
2. B. Böttcher, A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process, Math. Nachr. 278 (2005) 1235-1241.
3. B. Böttcher, Construction of time inhomogeneous Markov processes via evolution equations using pseudo-differential operators, to appear in J. Lond. Math. Soc.
4. B. Böttcher, Feller processes: The next generation in financial modeling, Brownian Motion, Lévy processes and beyond, preprint.
5. B. Böttcher and N. Jacob, Remarks on Meixner-type processes, in Probabilistic Methods in Fluids, eds. I. M. Davies et al. (World Scientific, 2003), pp. 35-47.
6. e sér. 88 (1964) 3-30.
7. S. E. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence (Wiley, 1986).
8. W. Hoh, Pseudo differential operators generating Markov processes, Habilitationsschrift, Universität Bielefeld, 1998.
9. W. Hoh, Private communication.
10. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Math. Library, Vol. 24 (2nd edn.) (North-Holland, 1989).
11. N. Jacob, Pseudo Differential Operators and Markov Processes, 3 Vols. (Imperial College Press, 2001-2005).
12. N. Jacob and R. L. Schilling, Lévy-type processes and pseudo-differential operators, in Lévy Processes: Theory and Applications, eds. O. E. Barndorff-Nielsen et al. (Birkhäuser, 2001), pp. 139-168.
13. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes Grundlehren Math. Wiss., Vol. 288 (2nd edn.) (Springer, 2002).
14. A. N. Kochubei, Parabolic pseudodifferential equations, hypersingular integrals and Markov processes, Math. USSR Izvestija 33 (1989) 233-259.
15. V. Kolokoltsov, Symmetric stable laws and stable-like jump-diffusions, Proc. London Math. Soc. 80 (2000) 725-768.
16. Z.-M. Ma, M. Röckner and T.-S. Zhang, Approximation of arbitrary Dirichlet processes by Markov chains, Ann. Inst. Poincaré 35 (1998) 1-22.
17. P. Protter and D. Talay, The Euler scheme for Lévy driven stochastic differential equations, Ann. Probab. 25 (1997) 393-423.
18. R.L. Schilling, Growth and Hölder conditions for the sample paths of Feller processes, Probab. Th. Relat. Fields 112 (1998) 565-611.
19. R. L. Schilling, Conservativeness and extensions of Feller semigroups, Positivity 2 (1998) 239-256.
20. D.W. Stroock, Diffusion processes associated with Levy generators, Probab. Th. Relat. Fields 32 (1975) 209-244.
21. D. W. Stroock, Markov Processes from K. Itô's Perspective, Ann. Math. Studies, Vol. 155 (Princeton Univ. Press, 2003).
22. M. Tsuchiya, Lévy measure with generalized polar decomposition and the associated SDE with jumps, Stoch. Stoch. Rep. 38 (1992) 95-117.