We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which...

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which...

Recent single-molecule fluorescence spectroscopy have been analyzed in terms of a reaction with a single fluctuating rate (Shenter, J. Phys. Chem A 103 (1999) 10477). The fluctuations in that analysis are related to the solution of an O–U equation. We propose the use of a simpler type of...

We develop the formalism for a continuous-time generalization of the persistent random walk, by allowing the sojourn time to deviate from the exponential form found in standard discussions of this subject. This generalization leads to evolution equations, in the time domain, that differ and are...

We present a method for finding statistical properties of the first passage time to exit an interval of general diffusion processes subject to random delta function impulses. Exact solutions are found for the mean first passage time for Brownian motion. Other special cases, detailed in the text,...

All definitions and analyses of the one-dimensional telegrapher's equation assume an underlying translational invariant space. We here generalize this model to allow for non-uniform spatial properties, and derive the form of the backward equation and the associated boundary conditions in the...

Recently Orsingher (1990) has derived bounds on the probability distribution of the maximum displacement of a one-dimensional diffusion process whose evolution is described by a telegrapher's equation. Foong has given more precise results for related variables. In this paper we derive an exact...

Most theoretical analyses of single-molecule spectroscopy (SMS) are formulated in terms of a first-order isomerization process. The mathematical problem to which the analysis reduces requires one to find the probability density for the total residence time in one of the states at a given...