Almost periodically unitary solutions to stochastic differential equations

Authors

  • O. Mellah Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria
  • K. Slimi Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria
  • M. Smaali Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria

DOI:

https://doi.org/10.31926/but.mif.2025.5.67.1.13

Keywords:

almost periodically unitary processes, stationary processes, stochastic differential equations, unitary group of operators

Abstract

In this paper, we consider a class of stochastic differential equations with almost periodic coefficients. In the one-dimensional case, by using the unitary group of operators associated to the stationary increments of the Brownian motion, we show the unitary almost periodicity of the solution. We also prove that the tightness is a property of almost periodically unitary processes. Some examples are given.

Author Biographies

O. Mellah, Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria

Laboratoire de Mathematiques Pures et Appliquees, Faculty of Sciences, 15000 

K. Slimi, Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria

Laboratoire de Mathematiques Pures et Appliquees, Faculty of Sciences, 15000

M. Smaali, Mouloud Mammeri University of Tizi Ouzou, Tizi Ouzou, Algeria

Laboratoire de Mathematiques Pures et Appliquees, Faculty of Sciences, 15000

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Published

2025-01-14

Issue

Vol. 5(67) No. 1 (2025)

Section

MATHEMATICS