Ja n 20 12 Central limit approximations for Markov population processes with countably many types

Central limit approximations for Markov population processes with countably many types

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic ...

Central and Local Limit Theories in Markov Dependent Random Variables

Central Limit Theorems and Diffusion Approximations for Multiscale Markov Chain Models1 by Hye-won Kang,

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple timescales, by a combination of the two. Motivated by models with multiple timescales arising in systems biology, we present a general approach to proving a central limit theorem cap...

Markov chain approximations for symmetric jump processes

Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space Rd the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space Hα/2(Rd), α ∈ (0, 2), that is equivalent to the standard one.

Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations

We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of infinite order. Combined with previous results on the rate of approximation this leads to a Central Limit Theorem for the bootstrapped estimator of the sample me...