Random difference equations: an asymptotical result
نویسندگان
چکیده
منابع مشابه
New Asymptotical Stability and Uniformly Asymptotical Stability Theorems for Nonautonomous Difference Equations
New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous differenc...
متن کاملRandom Difference Equations with Subexponential Innovations∗
In this paper we consider the random difference equations S =d (X + S)Y and T =d X+TY , where =d denotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right-hand side are independent of (X,Y ). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at...
متن کاملAn Asymptotic Result for Some Delay Difference Equations with Continuous Variable
We consider a nonhomogeneous linear delay difference equation with continuous variable and establish an asymptotic result for the solutions. Our result is obtained by the use of a positive root with an appropriate property of the so-called characteristic equation of the corresponding homogeneous linear (autonomous) delay difference equation. More precisely, we show that, for any solution, the l...
متن کاملA Law of Large Numbers for Rescaled Random Difference Equations∗
Abstract: We study the behaviour of stochastic processes defined as an iterated function system Xn+1 = Xn + af(Xn, Un+1) with initial value X0 = x0 and a stationary ergodic input signal (Un)n≥0 for small values of the parameter a. We obtain almost sure convergence of the path to the solution of the corresponding deterministic dynamical system defined by ẏ = F (y), where F (y) = E(f(y, U)). The ...
متن کاملRandom fractional functional differential equations
In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00821-x