TY - JOUR
T1 - Density of generalized Verhulst process and Bessel process with constant drift
AU - Cui, Zhenyu
AU - Nguyen, Duy
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - In this paper, we derive exact closed-form density functions of the generalized Verhulst process and the Bessel process with constant drift, which have applications in mathematical biology and queueing theory. We propose a generic probabilistic method for deriving exact closed-form density functions for these two diffusion processes based on a novel application of the exponential measure change in [T. Hurd and A. Kuznetsov, Explicit formulas for Laplace transforms of stochastic integrals, Markov Process. Relat. Fields, 14(2):277–290, 2008], together with formulae in [A. Borodin and P. Salminen, Handbook of Brownian Motion – Facts and Formulae, Birkhäuser, Basel, 2015]. Our study generalizes several known results in the literature.
AB - In this paper, we derive exact closed-form density functions of the generalized Verhulst process and the Bessel process with constant drift, which have applications in mathematical biology and queueing theory. We propose a generic probabilistic method for deriving exact closed-form density functions for these two diffusion processes based on a novel application of the exponential measure change in [T. Hurd and A. Kuznetsov, Explicit formulas for Laplace transforms of stochastic integrals, Markov Process. Relat. Fields, 14(2):277–290, 2008], together with formulae in [A. Borodin and P. Salminen, Handbook of Brownian Motion – Facts and Formulae, Birkhäuser, Basel, 2015]. Our study generalizes several known results in the literature.
KW - Bessel process with constant drift
KW - Verhulst process
KW - exponential change of measure
KW - geometric Brownian motion
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U2 - 10.1007/s10986-016-9329-9
DO - 10.1007/s10986-016-9329-9
M3 - Article
AN - SCOPUS:84994403133
SN - 0363-1672
VL - 56
SP - 463
EP - 473
JO - Lithuanian Mathematical Journal
JF - Lithuanian Mathematical Journal
IS - 4
ER -