Path Diffusion, Part I

28 Pages Posted: 24 May 2014

See all articles by Johan G. B. Beumee

Johan G. B. Beumee

JODE GROUP LTD

Christopher Cormack

Independent; UK Centre for Greening Finance and Investment (CGFI)

Peyman Khorsand

Independent

Manish K. Patel

Independent

Date Written: May 20, 2014

Abstract

This paper investigates the position (state) distribution of the single step binomial (multinomial) 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 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.

Keywords: Markov Process, Velocit Convexity Equation, Telegraph Equation, Klein-Gordon Equation, Newston's Equation

JEL Classification: C0, C6

Suggested Citation

Beumee, Johan and Cormack, Christopher and Khorsand, Peyman and Patel, Manish K., Path Diffusion, Part I (May 20, 2014). Available at SSRN: https://ssrn.com/abstract=2439187 or http://dx.doi.org/10.2139/ssrn.2439187

Johan Beumee (Contact Author)

JODE GROUP LTD ( email )

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Christopher Cormack

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UK Centre for Greening Finance and Investment (CGFI) ( email )

United Kingdom

Peyman Khorsand

Independent ( email )

Manish K. Patel

Independent ( email )

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