A brownian motion with two reflecting barriers and markov-modulated speed

Offer Kella*, Wolfgang Stadje

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider a Brownian motion with time-reversible Markov-modulated speed and two reflecting barriers. A methodology depending on a certain multidimensional martingale together with some linear algebra is applied in order to explicitly compute the stationary distribution of the joint process of the content level and the state of the underlying Markov chain. It is shown that the stationary distribution is such that the two quantities are independent. The long-run average push at the two barriers at each of the states is also computed.

Original languageAmerican English
Pages (from-to)1237-1242
Number of pages6
JournalJournal of Applied Probability
Volume41
Issue number4
DOIs
StatePublished - Dec 2004

Keywords

  • Brownian motion
  • Double barrier
  • Markov modulated
  • Multidimensional martingale
  • Reflected Brownian motion
  • State-dependent speed
  • Two-sided reflection

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