On a random number of disorders
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and random. It means that at two random successive moments (they can be equal also and equal zero too) the source of observations is changed and the first observation in new segment is chosen according to new transition probability starting from the last state of the previous segment. In effect the number of homogeneous segments is random. The transition probabilities of each process are known and a priori distribution of the disorder moments is given. The former research on such problem has been devoted to various questions concerning the distribution changes. The random number of distributional segments creates new problems in solutions with relation to analysis of the model with deterministic number of segments. Two cases are presented in details. In the first one the objectives is to stop on or between the disorder moments while in the second one our objective is to find the strategy which immediately detects the distribution changes. Both problems are reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function.
|Date of creation:||23 Nov 2008|
|Date of revision:||02 Jan 2010|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bojdecki, Tomasz & Hosza, Jerzy, 1984. "On a generalized disorder problem," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 349-359, November.
- Sarnowski, Wojciech & Szajowski, Krzysztof, 2008. "On-line detection of a part of a sequence with unspecified distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2511-2516, October.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:20256. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.