We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

The “first passage-time” problem is an important problem with a wide range of applications in mathematics, physics, biology and finance. Mathematically, such a problem can be reduced to estimating the probability of a (stochastic) process first to reach a critical level or threshold. While in other areas of applications the FPT problem can often be solved analytically, in finance we usually hav...

<p style='text-indent:20px;'>We present a non-intrusive model order reduction (NIMOR) approach with an offline-online decoupling for the solution of parameterized time-domain Maxwell's equations. During offline stage, training parameters are chosen by using Smolyak sparse grid method approximation level <inline-formula><tex-math id="M1">\begin{document}$ L $\end{document}</...

The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with jump-diffusion. While the application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, it becomes computationally ine...

The First-Passage Time (FPT) problems have numerous practical applications in fields that go from engineering and physics to finance and biology among many others. For the case of Markov gamma processes, this paper develops a methodology that combines the first Pontryagin equation approach and the cumulant analysis in order to obtain FPT statistics. For investigation about the structure of the ...

Climate prediction experiences various input uncertainties such as initial condition errors (predictability of the first kind), boundary condition (or model parameter) errors (predictability of the second kind), and combined errors (predictability of the third kind). Quantification of model predictability due to input uncertainties is a key issue leading to successful climate prediction. The fi...

We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias is constant. When the bias depends linearly on the position, the full FPT density function is derived in terms of Hermite polynomials and generalized Mittag-...

Many problems in finance require the information on the first passage time (FPT) of a stochastic process. Mathematically, such problems are often reduced to the evaluation of the probability density of the time for such a process to cross a certain level, a boundary, or to enter a certain region. While in other areas of applications the FPT problem can often be solved analytically, in finance w...

Aging has considerable effects on the appearance of the human face and is difficult to simulate using a universallyapplicable global aging model. In this paper, we focus on the hypothesis that the patterns of age progression (and regression) are related to the face concerned, as the latter implicitly captures the characteristics of gender, ethnic origin, and age group, as well as possibly the l...