A STOCHASTIC MODEL OF THE EVOLUTION DERIVED FROM ELASTIC VELOCITY PROCESS WITH MIXED DIFFUSION-JUMP CHARACTERISTICS-Reference-Cited by-同舟云学术

A STOCHASTIC MODEL OF THE EVOLUTION DERIVED FROM ELASTIC VELOCITY PROCESS WITH MIXED DIFFUSION-JUMP CHARACTERISTICS

Published:2002-07 Issue:07 Volume:12 Page:921-941
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

PAPIEZ LECH¹,TULOVSKY VLADIMIR²

Affiliation:

1. Department of Radiation Oncology, Indiana University, Medical Center, 535 Barnhill Drive, Indianapolis, IN 46202, USA

2. Division of Mathematics, Computer and Natural Sciences, St. John's University, 300 Howard Ave, Staten Island, NY 10306, USA

Abstract

The phenomenon of phase space evolution is modeled by the diffusional change in particles directions that is interrupted by independent collisions. Transition densities of stochastic process defined by this dynamical evolution are equivalent to solutions of a particular Boltzmann integro-differential equation. The general construction of solutions of this equation is developed. Specific methods of calculations of transition densities are detailed for the small angle approximation of the Boltzmann equation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202502001969

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