The Annals of Applied Probability

Multisource Bayesian sequential change detection

Savas Dayanik, H. Vincent Poor, and Semih O. Sezer

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Suppose that local characteristics of several independent compound Poisson and Wiener processes change suddenly and simultaneously at some unobservable disorder time. The problem is to detect the disorder time as quickly as possible after it happens and minimize the rate of false alarms at the same time. These problems arise, for example, from managing product quality in manufacturing systems and preventing the spread of infectious diseases. The promptness and accuracy of detection rules improve greatly if multiple independent information sources are available. Earlier work on sequential change detection in continuous time does not provide optimal rules for situations in which several marked count data and continuously changing signals are simultaneously observable. In this paper, optimal Bayesian sequential detection rules are developed for such problems when the marked count data is in the form of independent compound Poisson processes, and the continuously changing signals form a multi-dimensional Wiener process. An auxiliary optimal stopping problem for a jump-diffusion process is solved by transforming it first into a sequence of optimal stopping problems for a pure diffusion by means of a jump operator. This method is new and can be very useful in other applications as well, because it allows the use of the powerful optimal stopping theory for diffusions.

Article information

Ann. Appl. Probab., Volume 18, Number 2 (2008), 552-590.

First available in Project Euclid: 20 March 2008

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Zentralblatt MATH identifier

Primary: 62L10: Sequential analysis
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 62C10: Bayesian problems; characterization of Bayes procedures 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Sequential change detection jump-diffusion processes optimal stopping


Dayanik, Savas; Poor, H. Vincent; Sezer, Semih O. Multisource Bayesian sequential change detection. Ann. Appl. Probab. 18 (2008), no. 2, 552--590. doi:10.1214/07-AAP463.

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  • Baron, M. and Tartakovsky, A. G. (2006). Asymptotic optimality of change-point detection schemes in general continuous-time models. Sequential Anal. 25 257–296.
  • Bayraktar, E., Dayanik, S. and Karatzas, I. (2005). The standard Poisson disorder problem revisited. Stochastic Process. Appl. 115 1437–1450.
  • Bayraktar, E., Dayanik, S. and Karatzas, I. (2006). Adaptive Poisson disorder problem. Ann. Appl. Probab. 16 1190–1261.
  • Borodin, A. N. and Salminen, P. (2002). Handbook of Brownian Motion—Facts and Formulae, 2nd ed. Birkhäuser, Basel.
  • Brémaud, P. (1981). Point Processes and Queues. Springer, New York.
  • Byington, C. S. and Garga, A. K. (2001). Handbook of Multisensor Data Fusion. CRC Press, Boca Raton, FL.
  • Cartea, I. and Figueroa, M. (2005). Pricing in electricity markets: A mean reverting jump diffusion model with seasonality. Appl. Math. Finance 12 313–335.
  • Çinlar, E. (2006). Jump-diffusions. Blackwell-Tapia Conference, 3–4 November 2006. Available at
  • Dayanik, S. and Sezer, S. O. (2006). Compound Poisson disorder problem. Math. Oper. Res. 31 649–672.
  • Gapeev, P. V. (2005). The disorder problem for compound Poisson processes with exponential jumps. Ann. Appl. Probab. 15 487–499.
  • Itô, K. and McKean, Jr., H. P. (1974). Diffusion Processes and Their Sample Paths. Springer, Berlin.
  • Karlin, S. and Taylor, H. M. (1981). A Second Course in Stochastic Processes. Academic Press, New York.
  • Kushner, H. J. and Dupuis, P. (2001). Numerical Methods for Stochastic Control Problems in Continuous Time, 2nd ed. Springer, New York.
  • Peskir, G. and Shiryaev, A. (2006). Optimal Stopping and Free Boundary Problems. Birkhäuser, Basel.
  • Peskir, G. and Shiryaev, A. N. (2002). Solving the Poisson disorder problem. In Advances in Finance and Stochastics (K. Sandmann and P. Schonbucher, eds.) 295–312. Springer, Berlin.
  • Polyanin, A. D. and Zaitsev, V. F. (2003). Handbook of Exact Solutions for Ordinary Differential Equations, 2nd ed. Chapman and Hall/CRC, Boca Raton, FL.
  • Shiryaev, A. N. (1978). Optimal Stopping Rules. Springer, New York.
  • Weron, R., Bierbrauer, M. and Trück, S. (2004). Modeling electricity prices: Jump diffusion and regime switching. Phys. A Statist. Mech. Appl. 336 39–48.