FRACTIONAL LINEAR BIRTH-DEATH STOCHASTIC PROCESS-AN APPLICATION OF HEUN'S DIFFERENTIAL EQUATION
Artikel i vetenskaplig tidskrift, 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

Författare

Hidetoshi Konno

University of Tsukuba

Imre Pazsit

Chalmers, Fysik, Subatomär fysik och plasmafysik

Reports on Mathematical Physics

0034-4877 (ISSN)

Vol. 82 1 1-20

Ämneskategorier

Beräkningsmatematik

Datorsystem

Matematisk analys

DOI

10.1016/S0034-4877(18)30062-4

Mer information

Senast uppdaterat

2018-10-18