Central Limit Theorem for a Class of Relativistic Diffusions

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Central and Local Limit Theories in Markov Dependent Random Variables

A Unifying Approach to Relativistic Diffusions and H-theorems

A new, wide class of relativistic stochastic processes is introduced. All relativistic processes considered so far in the literature (the Relativistic Ornstein-Uhlenbeck Process as well as the Franchi-Le Jan and the Dunkel-Hänggi processes) are members of this class. The stochastic equations of motion and the associated forward Kolmogorov equations are obtained for each process in the class. Th...

Particle Filters for Partially Observed Diffusions

In this paper we introduce a novel particle filter scheme for a class of partiallyobserved multivariate diffusions. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson process whose intensity is a known function of the diffusion (Cox process). Unlike currentl...