Note on linear difference equations

Linear Difference Equations

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

A note on asymptotics and nonoscillation of linear q-difference equations

We study the linear second order q-difference equation y(q2t) + a(t)y(qt) + b(t)y(t) = 0 on the q-uniform lattice {qk : k ∈ N0} with q > 1, where b(t) 6= 0. We establish various conditions guaranteeing the existence of solutions satisfying certain estimates resp. (non)oscillation of all solutions resp. q-regular boundedness of solutions resp. q-regular variation of solutions. Such results may p...

Linear difference and differential equations

Semi-linear Stochastic Difference Equations

We consider in this paper a class of vector valued processes that have the form Yn+1 = An(Yn)+ Bn. Bn is assumed to be stationary ergodic and An is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability dist...

A note on asymptotic stability conditions for delay difference equations

We obtain necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation x n+1 + p N j=1 x n−k+(j−1)l = 0, where n = 0,1,2,..., p is a real number, and k, l, and N are positive integers such that k > (N − 1)l.