Exponential stability for nonlinear filtering

Exponential stability for nonlinear ltering

We study the a.s. exponential stability of the optimal lter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the lter) for a general setting both in discrete and in continuous time, in terms of Birkhoo's contraction coeecient. Criteria for exponential stability and explicit bounds on the rate are given in the speciic cases of a di...

Exponential Stability in Discrete Time Filtering for Non-Ergodic Signals

In this paper we prove exponential asymptotic stability for discrete time filters for signals arising as solutions of d-dimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of sufficiently small variance. The model for the signal admits non-ergodic processes. We show that almost surely, the total variation distance between the o...

Exponential Stability in a Nonlinear String Equation

We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

Exponential Stability in Nonlinear Difference Equations

Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee exponential stability of the zero solution of a nonlinear discrete system. The theory is illustrated with several examples.

Exponential stability for a nonlinear functional differential equation