Ergodic limits for inhomogeneous evolution equations

Almost Periodicity of Inhomogeneous Parabolic Evolution Equations

Are there ergodic limits to evolution? Ergodic exploration of genome space and convergence.

We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity-the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evo...

Uncomputably Noisy Ergodic Limits

V’yugin [2, 3] has shown that there are a computable shift-invariant measure on 2 and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages Anf . Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex...

On truncations for weakly ergodic inhomogeneous birth and death processes

We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bo...

Inhomogeneous Fractional Diffusion Equations

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...