Related papers: Coupled Continuous Time Random Maxima
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…
In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…
A continuous-time Markov chain (CTMC) execution is a continuous class of probability distributions over states. This paper proposes a probabilistic linear-time temporal logic, namely continuous-time linear logic (CLL), to reason about the…
Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few.…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price…
We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Rare events refer to qualitatively unlikely events whose realization can nevertheless have important consequences. Typically, the prediction of the kinetics of these events relies on Arrhenius laws, with exponentially distributed waiting…
Continuous-time Markov chains (CTMCs) are popular modeling formalism that constitutes the underlying semantics for real-time probabilistic systems such as queuing networks, stochastic process algebras, and calculi for systems biology. Prism…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
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…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Having reliable estimates of the occurrence rates of extreme events is highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period,…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The non-trivial incorporation of the reaction process into the CTRW is achieved by…