Abstract
Abstract In this paper, we investigate the asymptotical behavior for a partial sum sequence of independent random variables, and we derive a law of the iterated logarithm type. It is worth to point out that the partial sum sequence needs not to be an independent increment process. As an application of the theory established, we also give a sufficient criterion on the almost sure oscillation of solutions for a class of second-order stochastic difference equation of neutral type.
Highlights
1 Introduction To date, the asymptotic behavior of the solutions to deterministic difference equations has been discussed in many papers
The asymptotic behavior of the solutions to stochastic difference equation was discussed in many papers, and there have been very fruitful achievements
Motivated by [ ], in this paper we investigate the oscillation of the solution for the following second-order nonlinear stochastic difference equation: r(k) X(k) + f (k)F X(k) = ξ (k + ), k =
Summary
The asymptotic behavior of the solutions to deterministic difference equations has been discussed in many papers. Among them there are many papers about the oscillation of the solutions to deterministic difference equations. There is little known about the oscillation of the solutions of stochastic difference equations.
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