Invariant measure for diffusions with jumps

Applied Mathematics and Optimization

Volumn 40, Issue 1, 1999, Pages 105-140

  Menaldi, J L ^a   Robin, M ^b  

^a WAYNE STATE UNIVERSITY   (United States)

^b CERN   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

GREEN'S FUNCTION; INTEGRODIFFERENTIAL EQUATIONS; INVARIANCE; MARKOV PROCESSES; MATHEMATICAL TRANSFORMATIONS; PROBABILITY DENSITY FUNCTION;

DIRICHLET PROBLEM; ERGODIC OPTIMAL CONTROL; JUMP DIFFUSION;

OPTIMAL CONTROL SYSTEMS;

EID: 0032637178     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900118     Document Type: Article

References (22)

1. Bensoussan A (1988) Perturbation Methods in Optimal Control, Wiley, New York
2. Bensoussan A, Lions JL (1982) Applications of Variationals Inequalities in Stochastic Control, North-Holland, Amsterdam
3. Bensoussan A, Lions JL (1984) Impulse Control and Quasi-Variational Inequalities, Gauthier-Villars, Paris
4. Borkar VS (1991) Topics in Controlled Markov Chains, Pitman Research Notes in Mathematics Series No 240, Longman, Essex
5. Crandall MG, Ishii H, Lions PL (1992) User's guide to viscosity solutions of second order partial differential equations, Bull Amer Math Soc 27:1-67
6. Ethier SN, Kurtz TG (1986) Markov Processes, Wiley, New York
7. Fleming WH, Soner HM (1992) Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York
8. Garroni MG, Menaldi JL (1992) Green Functions for Second Order Integral-Differential Problems, Pitman Research Notes in Mathematics Series No 275, Longman, Essex
9. Gikhman II, Skorokhod AV (1972) Stochastic Differential Equations, Springer-Verlag, Berlin
10. Gilbarg D, Trudinger NS (1983) Elliptic Partial Differential Equations of Second Order, second edition, Springer-Verlag, New York
11. Gimbert F, Lions PL (1984) Existence and regularity results for solutions of second order, elliptic, integro-differential operators, Ricerche Mat, 33:315-358
12. Khasminskii RZ (Hasminskii) (1980) Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, Alphen aan den Rijn
13. Krylov NV (1987) Nonlinear Elliptic and Parabolic Equations of Second Order, Reidel, Dordrecht
14. Ladyzhenskaya OA, Uraltseva NN (1968) Linear and Quasilinear Elliptic Equations, Academic Press, New York
15. Lions PL (1982) A remark on bony maximum principle, Proc Amer Math Soc 88:503-508
16. Menaldi JL (1980) On the stopping time problem for degenerate diffusions, SIAM J Control Optim 18:697-721
17. Menaldi JL (1987) Optimal impulse control problems for degenerate diffusions with jumps, Acta Appl Math 8:165-198
18. Menaldi JL, Robin M (1997) Ergodic control of reflected diffusions with jumps, Appl Math Optim 35:117-137
19. Menaldi JL, Robin M (1999) On optimal ergodic control of diffusions with jumps, in Stochastic Analysis, Control, Optimization and Applications (a volume in honor of WH Fleming), McEneaney WM, Yin GG, Zhang Q (editors), Birkhäuser, Boston, pp 439-456
20. Protter MH, Weinberger HF (1984) Maximum Principles in Differential Equations, second edition, Springer-Verlag, New York
21. Robin M (1983) Long-term average cost control problems for continuous time Markov processes: a survey, Acta Appl Math 1:281-299
22. Stroock DW, Varadhan SR (1979) Multidimensional Diffusion Process, Springer-Verlag, Berlin