Disorder problem

In the study of stochastic processes in mathematics, a disorder problem or quickest detection problem (formulated by Kolmogorov) is the problem of using ongoing observations of a stochastic process to detect as soon as possible when the probabilistic properties of the process have changed. This is a type of change detection problem.

An example case is to detect the change in the drift parameter of a Wiener process.^[1]

Notes

1. Shiryaev (2007) page 208

References

• H. Vincent Poor and Olympia Hadjiliadis (2008). Quickest Detection (First ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-62104-5.
• Shiryaev, Albert N. (2007). Optimal Stopping Rules. Springer. ISBN 3-540-74010-4.
• Gapeev, P.V. (2005) The disorder problem for compound Poisson processes with exponential jumps. Ann. Appl. Probab. Volume 15, Number 1A, 487–499.
• Kolmogorov, A. N., Prokhorov, Yu. V. and Shiryaev, A. N. (1990). Methods of detecting spontaneously occurring effects. Proc. Steklov Inst. Math. 1, 1–21.