6,451 research outputs found
First passage time problem for biased continuous-time random walks
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-Leffler functions.Comment: 12 page
Appropriateness of correlated first order auto-regressive processes for modeling daily temperature records
The present study investigates linear and volatile (nonlinear) correlations
of first-order autoregressive process with uncorrelated AR (1) and long-range
correlated CAR (1) Gaussian innovations as a function of the process parameter
(). In the light of recent findings \cite{jano}, we discuss the choice
of CAR (1) in modeling daily temperature records. We demonstrate that while CAR
(1) is able to capture linear correlations it is unable to capture nonlinear
(volatile) correlations in daily temperature records.Comment: Accepted for publication in Physica
First Passage Time Distribution for Anomalous Diffusion
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 exemplified by the fractional Brownian motion, we show that the two
types of anomalous diffusions give rise to two distinct scaling behavior.Comment: 11 pages, 2 figure
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