Large deviations for small noise diffusions with discontinuous statistics

Probability Theory and Related Fields

Volumn 116, Issue 1, 2000, Pages 125-149

  Boué, Michelle ^a   Dupuis, Paul ^b   Ellis, Richard S ^c  

^a INSTITUTO TECNOLÓGICO AUTÓNOMO DE MÉXICO   (Mexico)

^b BROWN UNIVERSITY   (United States)

^c UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Discontinuous statistics; Large deviations; Small noise diffusions

Indexed keywords

EID: 0034424640     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008720     Document Type: Article

References (13)

1. Anderson, P., Orey, S.: Small random perturbations of dynamical systems with reflecting boundary. Nagoya Mathematical Journal. 60, 189-216, (1976)
2. Billingsley, P.: Convergence of Probability Measures. John Wiley & Sons, New York (1968)
3. Boué, M., Dupuis, P.: A variational representation for certain functionals of Brownian motion. Ann. Probab. 26, 1641-1659, (1998)
4. Chiang, T.S., Sheu, S.J.: Large deviation of diffusion processes and occupation times with discontinuous drift. Preprint (1997)
5. Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons (1997)
6. Dupuis, P., Ellis, R.S.: The large deviation principle for a general class of queueing systems, I. Trans. Amer. Math. Soc. 347, 2689-2751, (1995)
7. Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. John Wiley & Sons New York (1986)
8. Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer-Verlag Berlin (1984)
9. Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Second edition. Springer-Verlag, New York (1991)
10. Korostelev, A.P., Leonov, S.L.: Action functional for diffusion processes with discontinuous drift (in Russian). Theory Probab. Appl., 37, 570-576, (1992)
11. Korostelev, A.P., Leonov, S.L.: Action functional for diffusions in discontinuous media, Probab. Theory and Related Fields. 94, 317-333, (1993)
12. Kushner, H.J.: Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic System Theory. MIT Press, Cambridge (1984)
13. Veretennikov, A.Ju.: On strong solutions and explicit formulas for solutions of stochastic integral equations. Math. USSR Sbornik. 39, 387-403, (1981)