A mathematical model for the atomic clock error in case of jumps

We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative solution that can be useful for clock simulation, prediction, and interpretation, as well as for the understanding of the impact of clock error in the overall system in which clocks may be inserted as, for example, the Global Satellite Navigation Systems

First passage times of two-correlated processes: analytical results for the Wiener process and a numerical method for diffusion processes

Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first crossing component and of the position of the second crossing component before its crossing time. First we show that these densities are solutions of a system of Volterra-Fredholm first kind integral equations. Then we propose a numerical algorithm to solve it and we describe how to use the algorithm to approximate the joint density of the first passage times. The convergence of the method is theoretically proved for bivariate diffusion processes. We derive explicit expressions for these and other quantities of interest in the case of a bivariate Wiener process, correcting previous misprints appearing in the literature. Finally we illustrate the application of the method through a set of examples.Comment: 18 pages, 3 figure

Joint densities of first hitting times of a diffusion process through two time dependent boundaries

Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$, $\forall t>t_0$. We study the joint distribution of the two random variables $T_a$ and $T_b$, first hitting times of the diffusion process through the two boundaries $a(t)$ and $b(t)$, respectively. We express the joint distribution of $T_a, T_b$ in terms of $P(T_a<t,T_a<T_b)$ and $P(T_bT_b)$ and we determine a system of integral equations verified by these last probabilities. We propose a numerical algorithm to solve this system and we prove its convergence properties. Examples and modeling motivation for this study are also discussed

Some exact results on Lindley process with Laplace jumps

We consider a Lindley process with Laplace distributed space increments. We obtain closed form recursive expressions for the density function of the position of the process and for its first exit time distribution from the domain $[0,h]$. We illustrate the results in terms of the parameters of the process. The work is completed by an open source version of the software

Absence of polyphenol oxidase in cynomorium coccineum, a widespread holoparasitic plant

Polyphenol oxidase (PPO, E.C. 1.14.18.1) is a nearly ubiquitous enzyme that is widely distributed among organisms. Despite its widespread distribution, the role of PPO in plants has not been thoroughly elucidated. In this study, we report for the absence of PPO in Cynomorium coccineum, a holoparasitic plant adapted to withstand unfavorable climatic conditions, growing in Mediterranean countries and amply used in traditional medicine. The lack of PPO has been demonstrated by the absence of enzymatic activity with various substrates, by the lack of immunohistochemical detection of the enzyme, and by the absence of the PPO gene and, consequently, its expression. The results obtained in our work allow us to exclude the presence of the PPO activity (both latent and mature forms of the enzyme), as well as of one or more genes coding for PPO in C. coccineum. Finally, we discuss the possible significance of PPO deficiency in parasitic plants adapted to abiotic stress