We study a stochastic process Xt which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is dXt=(nD/X t)dt+√2DdWt, where Wt is the Wiener process. The drift term can arise from a logarithmic potential or from taking Xt as the norm of a multidimensional random walk. Due to the singularity of the drift term for Xt=0, different natures of boundary at the origin arise depending on the real parameter n: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary. © 2011 American Physical Society.
Edgar Martin, Ulrich Behn, Guido Germano
Physical Review E, (83)5, 051115.
Computational Finance, Computational Science, Data Science, Economics, Finance, and Financial markets