LINEAR DIFFERENCE EQUATIONS WITH A TRANSITION POINT AT THE ORIGIN

Linear difference equations with transition points

Two linearly independent asymptotic solutions are constructed for the second-order linear difference equation yn+1(x)− (Anx+ Bn)yn(x) + yn−1(x) = 0, where An and Bn have power series expansions of the form An ∼ ∞ ∑ s=0 αs ns , Bn ∼ ∞ ∑ s=0 βs ns with α0 = 0. Our results hold uniformly for x in an infinite interval containing the transition point x+ given by α0x++β0 = 2. As an illustration, we p...

A finite difference method for the smooth solution of linear Volterra integral equations

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

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...

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...