FRACTIONAL LINEAR BIRTH-DEATH STOCHASTIC PROCESS-AN APPLICATION OF HEUN'S DIFFERENTIAL EQUATION
Journal article, 2018

The method of Heun's differential equation is demonstrated in studying a fractional linear birth-death process (FLBDP) with long memory described by a master equation. The exact analytic solution of the generating function for the probability density is obtained on the basis of Heun's differential equation. The multi-fractal nature of FLBDP associated with long memory is demonstrated in conjunction with the present simple birth death process. Finally, the subtle multi-fractal nature of critical fluctuations under long memory is also displayed in the present FLBDP. Further, discussions are also given on the features of transient fluctuation in systems with long memory.

master equation

generating function

the waiting time (lifetime) distribution

fractional linear birth-death process

critical fluctuations

Author

Hidetoshi Konno

University of Tsukuba

Imre Pazsit

Chalmers, Physics, Subatomic and Plasma Physics

Reports on Mathematical Physics

0034-4877 (ISSN)

Vol. 82 1 1-20

Subject Categories

Computational Mathematics

Computer Systems

Mathematical Analysis

DOI

10.1016/S0034-4877(18)30062-4

More information

Latest update

10/18/2018