Relative Controllability of Linear Difference Equations

Relative invariants , difference equations , and

Acknowledgements First of all I would like to thank my supervisor Professor T. Kimura. He taught me how to learn mathematics from the beginning when I just started afresh my life. About four years ago he suggested to study on archimedean local zeta functions of several variables as my first research task for the Master's thesis. I can not give enough thanks to his heartwarming encouragement all...

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 ug 2 01 7 Approximate and exact controllability of linear difference equations ∗

In this paper, we study approximate and exact controllability of the linear difference equation x(t) = ∑Nj=1A jx(t −Λ j) +Bu(t) in L2, with x(t) ∈ C and u(t) ∈ C, using as a basic tool a representation formula for its solution in terms of the initial condition, the control u, and some suitable matrix coefficients. When Λ1, . . . ,ΛN are commensurable, approximate and exact controllability are e...

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...