We propose a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: The first, which we largely focus on, features a random quantile level and allows for direct interpretation...

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the...

A subthreshold signal is transmitted through a channel and may be detected when some noise - with known structure and proportional to some level - is added to the data. There is an optimal noise level, called stochastic resonance, that corresponds to the highest Fisher information in the problem...

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In...

In the past several decades, new-product diffusion models has been an active area of research in marketing (see, e.g., Mahajan, Muller, and Wind 2000, and Mahajan and Wind 1986). Such models are useful because they can provide important insights into the timing of initial purchase of new...

This paper presents analytical expressions for the mobility ( [[EQUATION]] ) and diffusion coefficient ( [[EQUATION]] ) of a chemical compound [[EQUATION]] that react with a carrier [[EQUATION]] giving a product [[EQUATION]] in the presence of drift. A one-dimensional lattice gas of [[EQUATION]]...