Almost sure convergence of solutions to non-homogeneous stochastic difference equation Academic Article

abstract

• We consider a non-homogeneous non-linear stochastic difference equationand its linear counterpartboth with initial value , non-random decaying free coefficient S n and independent random variables . We establish results on a.s. convergence of solutions X n to zero. Obtained necessary conditions tie together certain moments of the noise and the rate of decay of S n . To ascertain sharpness of our conditions we discuss some situations when X n diverges. We also establish a result concerning the rate of decay of X n to zero. Several examples are given to illustrate the ideas of the paper.

authors

• Berkolaiko, Gregory

published proceedings

• JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS

author list (cited authors)

• Berkolaiko, G., & Rodkina, A.

citation count

• 12

publication date

• June 2006

publisher

• Taylor & Francis  Publisher

keywords

• Almost Sure Stability
• Martingale Convergence Theorem
• Non-linear Stochastic Difference Equations
• Random Variables

Digital Object Identifier (DOI)

• 10.1080/10236190600574093

start page

• 535

end page

• 553

volume

• 12

issue

• 6

URL

• http://dx.doi.org/10.1080/10236190600574093