Bayesian sequential testing problem for a Brownian bridge
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 683-712
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The present paper gives a solution to the Bayesian sequential testing problem
of two simple hypotheses about the mean of a Brownian bridge. The method of
the proof is based on reducing the sequential analysis problem to the
optimal stopping problem for a strong Markov posterior probability process.
The key idea in solving the above problem is the application of the
one-to-one Kolmogorov time-space transformation, which enables one to
consider, instead of the optimal stopping problem on a finite time horizon
for a time-inhomogeneous diffusion process, an optimal stopping problem on an
infinite time horizon for a homogeneous diffusion process with a slightly
more complicated risk functional. The continuation and stopping sets are
determined by two continuous boundaries, which constitute a unique solution
of a system of two nonlinear integral equations.
Keywords:
sequential analysis, hypothesis testing problem, optimal stopping problem, Brownian bridge,
Kolmogorov time-space transformation.
@article{TVP_2018_63_4_a3,
author = {D. I. Lisovskii},
title = {Bayesian sequential testing problem for a {Brownian} bridge},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {683--712},
publisher = {mathdoc},
volume = {63},
number = {4},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a3/}
}
D. I. Lisovskii. Bayesian sequential testing problem for a Brownian bridge. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 683-712. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a3/