Hypertranscendence and 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...

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...

Difference integrability conditions for parameterized linear difference and differential equations

This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference isomonodromic with respect to each parameter separately. Due to this result, it is no longer necessary to solve non-linear difference equations to verify isomonodromici...

Combinatorial Recurrences and Linear Difference Equations

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appe...