Periodic Ornstein-Uhlenbeck processes driven by Lévy processes

Journal of Applied Probability

Volumn 39, Issue 4, 2002, Pages 748-763

  Pedersen, Jan ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

L vy processes; Ornstein Uhlenbeck processes; Periodic processes; Self decomposable distributions

Indexed keywords

EID: 0036998468     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1037816016     Document Type: Article

References (11)

1. ALABERT, A., FERRANTE, M. AND NUALART, D. (1995). Markov field property of stochastic differential equations. Ann. Prob. 23, 1262-1288.
2. BARNDORFF-NIELSEN, O. E. AND SHEPHARD, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. R. Statist. Soc. B 63, 167-241.
3. GRENANDER, U. (1993). General Pattern Theory. A Mathematical Study of Regular Structures. Oxford University Press.
4. HOBOLTH, A. AND JENSEN, E. B. V. (2000). Modelling stochastic changes in curve shape, with an application to cancer diagnostics. Adv. Appl. Prob. 32, 344-362.
5. KWAKERNAAK, H. (1975). Periodic linear differential stochastic processes. SIAM J. Control Optimization 13, 400-413.
6. NORRIS, J. R. (1998). Ornstein-Uhlenbeck processes indexed by the circle. Ann. Prob. 26, 465-478.
7. NUALART, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York.
8. OCONE, D. AND PARDOUX, É. (1989). Linear stochastic differential equations with boundary conditions. Prob. Theory Relat. Fields 82, 489-526.
9. Rælly, S. and Thieullen, M. (2002). A characterization of reciprocal processes via an integration by parts formula on the path space. Prob. Theory Relat. Fields 123, 97-120.
10. ROCHA-ARTEAGA, A. AND SATO, K. (2001). Topics in infinitely divisible distributions and Lévy processes. Comun. Téc. I-01-15, CIMAT, Guanajuato.
11. SATO, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.