Degenerate Cocycle With Index-1 and Lyapunov Exponents

Abstract

This paper deals with the solvability of initial-value problem and with Lyapunov exponents for linear implicit random difference equations, i.e. the difference equations where the leading term cannot be solved. An index-1 concept for linear implicit random difference equations is introduced and a formula of solutions is given. Paper is also concerned with a version of the multiplicative theorem of Oseledets type.

Stability Radii for Implicit Difference Equations

“…In fact, we are concerned with a so-called ill-posed problem where the solutions of Cauchy problem may exist only on a submanifold or even they do not exist. According to [5], it is necessary to impose some further assumptions stated under the form of indices of the equation.…”

A Comparison Theorem for Stability of Linear Stochastic Implicit Difference Equations of Index-1

“…ii are used for the index-1 concept for implicit difference equations, see [15][16][17]. This natural restriction…”