Complex Differences and Difference Equations

ISOMONODROMY FOR COMPLEX LINEAR q-DIFFERENCE EQUATIONS

— The words “monodromy” and “isomonodromy” are used in the theory of difference and q-difference equations by Baranovsky-Ginzburg, Jimbo-Sakai, Borodin, Krichever,... although it is not clear that phenomena of branching during analytic continuation are involved there. In order to clarify what is at stake, we survey results obtained during the last few years, mostly by J.-P. Ramis, J. Sauloy and...

A Variational Complex for Difference Equations

On Third-order Linear Difference Equations Involving Quasi-differences

had been investigated. As it is noted here, these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linear nth-order difference equations with quasi-differences. Such equations have been widely studied in the literature, see, for example, [6, 11] and the references therein. The natural question which arises is to find the adjoi...

On Some Solvable Difference Equations and Systems of Difference Equations

AND APPLIED ANALYSIS, Vol. 2012, No. Article ID 54176, pp. 1-11, Nov, 2012 References: Abstract: Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.

The Stationary - NonStationary Process and The Variable Roots Difference Equations

Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...