Hereditary systems (or systems with either delay or after-effects) are
widely used to model processes in physics, mechanics, control, economics
and biology. An important element in their study is their stability.
Stability conditions for difference equations with delay can be obtained
using a Lyapunov functional.
Lyapunov Functionals and Stability of Stochastic Difference Equations
describes a general method of Lyapunov functional construction to
investigate the stability of discrete- and continuous-time stochastic
Volterra difference equations. The method allows the investigation of
the degree to which the stability properties of differential equations
are preserved in their difference analogues.
The text is self-contained, beginning with basic definitions and the
mathematical fundamentals of Lyapunov functional construction and moving
on from particular to general stability results for stochastic
difference equations with constant coefficients. Results are then
discussed for stochastic difference equations of linear, nonlinear,
delayed, discrete and continuous types. Examples are drawn from a
variety of physical systems including inverted pendulum control, study
of epidemic development, Nicholson's blowflies equation and
predator-prey relationships.
Lyapunov Functionals and Stability of Stochastic Difference Equations is
primarily addressed to experts in stability theory but will also be of
use in the work of pure and computational mathematicians and researchers
using the ideas of optimal control to study economic, mechanical and
biological systems.
