Infinite product expansion of the Fokker-Planck equation with steady-state solution.
We present an analytical technique for solving Fokker-Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.
Apollo Global Management International LLP , 25 St George Street, London W1S 1FS, UK ; Department of Mathematics , Imperial College London , South Kensington, London SW7 2AZ, UK.
R J
RJ
Martin
Department of Mathematics , Imperial College London , South Kensington, London SW7 2AZ, UK.
R V
0000-0001-9799-9639
RV
Craster
Faculty of Engineering and Physical Sciences, University of Surrey , Guildford GU2 7XH, UK.
M J
MJ
Kearney
Ornstein–Uhlenbeck process; asymptotics; diffusion; infinite product; mathematical finance