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This article is cited in 1 scientific paper (total in 1 paper)
Short Communications
On a formulation of the multiple “disorder” problem
A. F. Nikolaev Ulyanovsk State University, Faculty of Mathematics and Mechanics
Abstract:
This paper deals with a formulation of the multiple "disorder" problem. Let $\tau_1,\ldots, \tau_n$ be “disorder” emergence times. Available for observation is a process $x$ with differential $dx_t = \theta_t \,dt +\sigma \,dW_t$, where $\theta_t = \sum_{i=1}^{n}a_i I\{t \ge \tau_i\}$ is a Markov process. Having the realization of the process $x$, it is required to estimate $\tau_i$, $i=1,\ldots,n$. The estimation of time $\tau_i$ is based on verifying the hypothesis about reaching the level $A_i = \sum_{k=1}^{i}a_k$ by the process $\theta$.
Keywords:
multiple “disorder” filtration for a Markov process with a countable number of states, decision function.
Received: 19.05.1997
Citation:
A. F. Nikolaev, “On a formulation of the multiple “disorder” problem”, Teor. Veroyatnost. i Primenen., 43:2 (1998), 370–374; Theory Probab. Appl., 43:2 (1999), 293–297
Linking options:
https://www.mathnet.ru/eng/tvp1473https://doi.org/10.4213/tvp1473 https://www.mathnet.ru/eng/tvp/v43/i2/p370
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Abstract page: | 250 | Full-text PDF : | 138 | First page: | 21 |
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