FRACTIONAL LINEAR BIRTH-DEATH STOCHASTIC PROCESS-AN APPLICATION OF HEUN'S DIFFERENTIAL EQUATION

被引：0

作者：

Konno, Hidetoshi ^{[1
]}

Pazsit, Imre ^{[2
]}

机构：

[1] Univ Tsukuba, 1-1-1 Ten Nou Dai, Tsukuba, Ibaraki 3058573, Japan

[2] Chalmers Univ Technol, Div Subat & Plasma Phys, SE-41296 Gothenburg, Sweden

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2018年 / 82卷 / 01期

关键词：

fractional linear birth-death process; master equation; generating function; the waiting time (lifetime) distribution; critical fluctuations; CONTINUOUS-TIME FINANCE; ROGUE WAVES; DIFFUSION; MODELS; FACTORIZATION; FIBRILLATION; CALCULUS;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1 / 20

页数：20

共 50 条

[1] Birth-Death Stochastic Process of Optical Rogue Wave Described by Fractional Master Equation - Application of Confluent Heun Differential Equation
Konno, Hidetoshi
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2017, 86 (06)
[2] On a fractional linear birth-death process
Orsingher, Enzo
Polito, Federico
[J]. BERNOULLI, 2011, 17 (01) : 114 - 137
[3] A STOCHASTIC GOMPERTZ BIRTH-DEATH PROCESS
TAN, WY
[J]. STATISTICS & PROBABILITY LETTERS, 1986, 4 (01) : 25 - 28
[4] THE LINEAR BIRTH-DEATH PROCESS: AN INFERENTIAL RETROSPECTIVE
Tavare, Simon
[J]. ADVANCES IN APPLIED PROBABILITY, 2018, 50 (0A) : 253 - 269
[5] On the Generalized Birth-Death Process and Its Linear Versions
Vishwakarma, P.
Kataria, K. K.
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2024,
[6] A Stochastic Simulator of Birth-Death Master Equations with Application to Phylodynamics
Vaughan, Timothy G.
Drummond, Alexei J.
[J]. MOLECULAR BIOLOGY AND EVOLUTION, 2013, 30 (06) : 1480 - 1493
[7] Integrability of stochastic birth-death processes via differential Galois theory
Acosta-Humanez, Primitivo B.
Capitan, Jose A.
Morales-Ruiz, Juan J.
[J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2020, 15
[8] COLMATAGE-SCOURING KINETICS IN LIGHT OF STOCHASTIC BIRTH-DEATH PROCESS
LITWINIS.J
[J]. BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES TECHNIQUES, 1966, 14 (09): : 907 - &
[9] GENERALIZED BIRTH-DEATH STOCHASTIC-PROCESS IN NONEQUILIBRIUM OPEN SYSTEM
KONNO, H
LOMDAHL, PS
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1995, 64 (06) : 1936 - 1944
[10] The birth-death stochastic processes of "solitons" in the 1D Benney equation
Konno, H
Lomdahl, PS
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2000, 69 (06) : 1629 - 1641

← 1 2 3 4 5 →