Adaptive poisson disorder problem

Annals of Applied Probability

Volumn 16, Issue 3, 2006, Pages 1190-1261

  Bayraktar, Erhan ^a   Dayanik, Savas ^b,d   Karatzas, Ioannis ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c Columbia University ^*  (United States)

^d Princeton University   (United States)

Author keywords

Optimal stopping; Poisson disorder problem; Quickest detection

Indexed keywords

EID: 33750534344     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051606000000312     Document Type: Article

References (17)

1. BAYRAKTAR, E. and DAYANIK, S. (2006). Poisson disorder problem with exponential penalty for delay. Math. Oper. Res. 31 217-233.
2. BAYRAKTAR, E., DAYANIK, S. and KARATZAS, I. (2004). Adaptive Poisson disorder problem. Working paper, Princeton Univ. Available at http://www.princeton.edu/~sdayanik/papers/bayes.pdf.
3. BAYRAKTAR, E., DAYANIK, S. and KARATZAS, I. (2005). The standard Poisson disorder problem revisited. Stochastic Process. Appl. 115 1437-1450. MR2158013
4. BEIBEL, M. (1997). Sequential change-point detection in continuous time when the postchange drift is unknown. Bernoulli 3 457-478. MR1483699
5. BEIBEL, M. and LERCHE, H. R. (2003). Sequential Bayes detection of trend changes. In Foundations of Statistical Inference (Y. Haitovsky, H. R. Lerche and Y. Ritov, eds.) 117-130. Physica, Heidelberg. MR2017819
6. BRÉMAUD, P. (1981). Point Processes and Queues. Springer, New York. MR8260058
7. CLARKE, F. H., LEDYAEV, Y. S., STERN, R. J. and WOLENSKI, P. R. (1998). Nonsmooth Analysis and Control Theory. Springer, New York. MR9949001
8. DAVIS, M. H. A. (1976). A note on the Poisson disorder problem. Banach Center Publ. 1 65-72.
9. DAVIS, M. H. A. (1993). Markov Models and Optimization. Chapman and Hall, London. MR1283589
10. GALCHUK, L. I. and ROZOVSKII, B. L. (1971). The disorder problem for a Poisson process. Theory Probab. Appl. 16 729-734. MR0297028
11. GUGERLI, U.S. (1986). Optimal stopping of a piecewise-deterministic Markov process. Stochastics 19 221-236. MR0872462
12. KRANTZ, S. G. and PARKS, H. R. (2002). The Implicit Function Theorem. Birkhäuser, Boston. MR0326001
13. LIPTSER, R. S. and SHIRYAEV, A. N. (2001). Statistics of Random Processes I. Springer, Berlin. MR0160001
14. ØKSENDAL, B. (1998). Stochastic Differential Equations. Springer, Berlin. MR9960119
15. PESKIR, G. and SHIRYAEV, A. N. (2002). Solving the Poisson disorder problem. In Advances in Finance and Stochastics (K. Sandmann and P. J. Schönbucher, eds.) 295-312. Springer, Berlin. MR1929384
16. PROTTER, M. H. and MORREY, JR., C. B. (1991). A First Course in Real Analysis, 2nd ed. Springer, New York. MR1123269
17. ROCKAFELLAR, R. T. (1997). Convex Analysis. Princeton Univ. Press. MR1451876