We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non-Markovian formulation of the CTRW aimed to...

An analysis based on the assumption that tick-by-tick data is linear may lead to incorrect conclusions if the underlying process is multiplicative. We compare data analysis done with return and stock differences and study the limits within which the two approaches are equivalent. Illustrative...

The present work briefly summarizes the results obtained in Palatella et al. Eur. Phys. J. B 38 (2004) 671 using the Diffusion Entropy technique and adds some new results regarding the Dow Jones Index time series. We show that time distances between peaks of volatility or activity are...

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...

A mathematical model suggested by Orsingher, motivated by possible applicability to diffusion processes in which anisotropic scattering is significant, is reanalyzed. It is shown that the propagator for the full multi-dimensional model does not satisfy a telegrapher's equation, as suggested by...