scholarly journals Behavior of solution of stochastic difference equation with continuous time under additive fading noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Leonid Shaikhet
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Stochastic Difference Equation

GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

2005 ◽  
Vol 05 (02) ◽  
pp. 175-188 ◽  
Author(s):  
LEONID SHAIKHET
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Continuous Time ◽  
Type Theorem ◽  
Volterra Equations ◽  
Lyapunov Functionals ◽  
Stochastic Difference Equation ◽  
Stochastic Difference Equations ◽  
After Effect ◽  
General Method

The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with after-effect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear as useful mathematical models. Here this method is used for a stability investigation of some nonlinear stochastic difference equation with continuous time.

Integer-valued branching processes with immigration

1983 ◽  
Vol 15 (04) ◽  
pp. 713-725 ◽  
Author(s):  
F. W. Steutel ◽  
W. Vervaat ◽  
S. J. Wolfe
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Queueing Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Discrete State ◽  
Limiting Behaviour ◽  
Supercritical Branching Processes

The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].

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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