The almost everywhere oscillations of the stochastic difference equation Δ2x(n) +f(n)F(x(n)) =ξ(n+ 2)

2014 ◽  
Author(s):  
Junshan Zeng ◽  
Sufang Han ◽  
Yao Lin ◽  
Zheng Yu
Keyword(s):  
Difference Equation ◽  
Stochastic Difference Equation ◽  
Almost Everywhere

scholarly journals On Tails of Perpetuities

2010 ◽  
Vol 47 (4) ◽  
pp. 1191-1194 ◽  
Author(s):  
Paweł Hitczenko
Keyword(s):  
Lower Bound ◽  
Difference Equation ◽  
Upper Bound ◽  
Random Variable ◽  
Stochastic Difference Equation

We establish an upper bound on the tails of a random variable that arises as a solution of a stochastic difference equation. In the nonnegative case our bound is similar to a lower bound obtained in Goldie and Grübel (1996).

Existence of moments in a stationary stochastic difference equation

1990 ◽  
Vol 22 (1) ◽  
pp. 129-146 ◽  
Author(s):  
Hans Arnfinn Karlsen
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Difference Equation ◽  
Dependent Variables ◽  
Gaussian Case ◽  
Necessary And Sufficient

The stationary stochastic difference equation Xt = YtXt–1 + Wt is analyzed with emphasis on conditions ensuring that ||Xt||p <∞. Some general results are obtained and then applied to different classes of input processes {(Yt, Wt)}. Especially both necessary and sufficient conditions are given in the Gaussian case. We also obtain results concerning moments of products of dependent variables.

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