The martingale problem for a class of stable-like processes

Stochastic Processes and their Applications

Volumn 119, Issue 4, 2009, Pages 1144-1167

  Bass, Richard F ^a   Tang, Huili ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Harnack inequality; Jump process; Martingale problem; Poisson point process; Stable like processes; Stochastic differential equation; Symmetric stable process

Indexed keywords

DIFFERENTIAL EQUATIONS; FARM BUILDINGS; MARKOV PROCESSES; MATHEMATICAL OPERATORS; MEASUREMENT THEORY; POISSON DISTRIBUTION; STABILITY CRITERIA; STOCHASTIC CONTROL SYSTEMS;

HARNACK INEQUALITY; JUMP PROCESS; MARTINGALE PROBLEM; POISSON POINT PROCESS; STABLE-LIKE PROCESSES; STOCHASTIC DIFFERENTIAL EQUATION; SYMMETRIC STABLE PROCESS;

POISSON EQUATION;

EID: 61849156395     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2008.06.003     Document Type: Article

References (17)

1. Athreya S.R., Barlow M.T., Bass R.F., and Perkins E.A. Degenerate stochastic differential equations and super-Markov chains. Probab. Theory Related Fields 123 4 (2002) 484-520
2. M.T. Barlow, R.F. Bass, Z.-Q. Chen, M. Kassmann, Non-local Dirichlet forms and symmetric jump processes, Trans. Amer. Math. Soc. (in press)
3. Bass R.F. Occupation time densities for stable-like processes and other pure jump Markov processes. Stochastic Process. Appl. 29 1 (1988) 65-83
4. Bass R.F. Uniqueness in law for pure jump Markov processes. Probab. Theory Related Fields 79 2 (1988) 271-287
5. Bass R.F. Diffusions and Elliptic Operators (1997), Springer, New York
6. Bass R.F., and Kassmann M. Harnack inequalities for non-local operators of variable order. Trans. Amer. Math. Soc. 357 (2005) 837-850
7. Bass R.F., and Kassmann M. Hölder continuity of harmonic functions with respect to operators of variable order. Comm. Partial Differential Equations 30 (2005) 1249-1259
8. R.F. Bass, M. Kassmann, T. Kumagai, Symmetric jump processes: Localization, heat kernels, and convergence, preprint
9. Bass R.F., and Levin D.A. Harnack inequalities for jump processes. Potential Anal. 17 4 (2002) 375-388
10. Chen Z.-Q., and Kumagai T. Heat kernel estimates for stable-like processes on d-sets. Stochastic Process. Appl. 108 1 (2003) 27-62
11. Jacod J. Calcul stochastique et problémes de martingales (1979), Springer, Berlin
12. Komatsu T. On the martingale problem for generators of stable processes with perturbations. Osaka J. Math. 21 1 (1984) 113-132
13. Lepeltier J.-P., and Marchal B. Probléme des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel. Ann. Inst. H. Poincaré Sect. B (N.S.) 12 1 (1976) 43-103
14. Meyer P.-A. Un cours sur les intégrales stochastiques. Séminaire de Probabilités X (1976), Springer, Berlin 245-400
15. Nadirashvili N. Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators. Ann. Scuola Norm. Sup. Pisa 24 3 (1997) 537-549
16. Song R., and Vondraček Z. Harnack inequality for some classes of Markov processes. Math. Z. 246 1-2 (2004) 177-202
17. Stroock D.W., and Varadhan S.R.S. Multidimensional Diffusion Processes (1979), Springer, New York