Disorder problem

In the study of stochastic processes in mathematics, a disorder problem (or quickest detection problem) has been formulated by Kolmogorov. Specifically, the problem is use ongoing observations on a stochastic process to decide whether or not to raise an alarm that the probabilistic properties of the process have changed.

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

Notes

1. ^ Shiryaev (2007) page 208

References

• H. Vincent Poor and Olympia Hadjiliadis (2008). Quickest Detection (First edition ed.). Cambridge: Cambridge University Press. ISBN 9780521621045. 
• Shiryaev, Albert N. (2007). Optimal Stopping Rules. Springer. ISBN 3540740104. 
• Gapeev, P.V. (2005) The disorder problem for compound Poisson processes with exponential jumps. Ann. Appl. Probab. Volume 15, Number 1A, 487–499. [1]
• Kolmogorov, A. N., Prokhorov, Yu. V. and Shiryaev, A. N. (1990). Methods of detecting spontaneously occurring effects. Proc. Steklov Inst. Math. 1, 1–21.

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