On a formulation of the multiple ``disorder'' problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 2, pp. 370-374
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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.
@article{TVP_1998_43_2_a11,
author = {A. F. Nikolaev},
title = {On a formulation of the multiple ``disorder'' problem},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {370--374},
publisher = {mathdoc},
volume = {43},
number = {2},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_2_a11/}
}
A. F. Nikolaev. On a formulation of the multiple ``disorder'' problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 2, pp. 370-374. http://geodesic.mathdoc.fr/item/TVP_1998_43_2_a11/