English

Sequential tracking of an unobservable two-state Markov process under Brownian noise

Probability 2019-08-06 v1 Statistics Theory Statistics Theory

Abstract

We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not observable, and the problem consist in finding a {-1,1}-valued process that tracks the unobservable process as close as possible. We present an explicit construction of such a process.

Keywords

Cite

@article{arxiv.1908.01162,
  title  = {Sequential tracking of an unobservable two-state Markov process under Brownian noise},
  author = {Alexey Muravlev and Mikhail Urusov and Mikhail Zhitlukhin},
  journal= {arXiv preprint arXiv:1908.01162},
  year   = {2019}
}

Comments

18 pages

R2 v1 2026-06-23T10:38:51.714Z