%0 Journal Article
%T Path Diffusion, Part I
%A Johan GB Beumee
%A Chris Cormack
%A Peyman Khorsand
%A Manish Patel
%J Quantitative Finance
%D 2014
%I arXiv
%X This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which also preserves the proper state equation of motion. Many numerical numerical examples of this process are provided. For a smaller grid the probability construction converges into a correlated set of probabilities of hyperbolic functions for each velocity at each state point. It is shown that the two dimensional process can be transformed into a Telegraph equation and via transformation into a Klein-Gordon equation if the transition rates are constant. In the last Section there is an example of multi-dimensional hyperbolic partial differential equation whose numerical average satisfies Newton's equation. There is also a momentum measure provided both for the two-dimensional case as for the multi-dimensional rate matrix.
%U http://arxiv.org/abs/1406.0077v1