A DIRECT SOLUTION TO THE FOKKER–PLANCK EQUATION FOR EXPONENTIAL BROWNIAN FUNCTIONALS

2010 ◽  
Vol 08 (03) ◽  
pp. 287-304 ◽  
Author(s):  
CAROLINE PINTOUX ◽  
NICOLAS PRIVAULT
Keyword(s):  
Integral Representation ◽  
Gamma Function ◽  
Planck Equation ◽  
Heat Kernels ◽  
Direct Solution ◽  
Spectral Expansions ◽  
Fokker Planck Equation ◽  
Financial Application ◽  
Exponential Brownian Functionals ◽  
Fokker Planck

The solution of the Fokker–Planck equation for exponential Brownian functionals usually involves spectral expansions that are difficult to compute explicitly. In this paper, we propose a direct solution based on heat kernels and a new integral representation for the square modulus of the Gamma function. A financial application to bond pricing in the Dothan model is also presented.

scholarly journals Extended Mellin integral representations for the absolute value of the gamma function

Analysis ◽  
2018 ◽  
Vol 38 (1) ◽  
pp. 11-20
Author(s):  
Nicolas Privault
Keyword(s):  
Fourier Transform ◽  
Gamma Function ◽  
Bessel Functions ◽  
Planck Equation ◽  
Integral Representations ◽  
Modified Bessel Functions ◽  
Absolute Value ◽  
Fokker Planck Equation ◽  
The Absolute ◽  
Fokker Planck

AbstractWe derive Mellin integral representations in terms of Macdonald functions for the squared absolute value{s\mapsto|\Gamma(a+is)|^{2}}of the gamma function and its Fourier transform when{a<0}is non-integer, generalizing known results in the case{a>0}. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of a Fokker–Planck equation.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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