On a stochastic process with switchings

Vladimir Ivanovich Lotov, Vali Raximdjanovich Xodjibayev

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1 Citation (Scopus)

Abstract

We study a stochastic process X(t) with switchings between two stationary processes with independent increments while achieving regulatory barriers. We obtain the dual Laplace-Stieltjes transform of the distribution of the process X(t) and its limit as t ! 1. Under Cramer's type conditions, the asymptotic representations of these transforms are obtained when the width of the regulating strip is growing. We use known results for regenerative processes and factorization technique for the study in boundary crossing problems for stochastic processes.

Translated title of the contributionО случайном процессе с переключениями
Original languageEnglish
Pages (from-to)1531-1546
Number of pages16
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Factorization method
  • Oscillating stochastic process
  • Regenerative process
  • Stationary distribution
  • Stationary process with independent increments

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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