The theory of scale functions for spectrally negative Lévy processes

S Cohen, A Kuznetsov, AE Kyprianou, V Rivero… - Lévy Matters II: Recent …, 2013‏ - Springer
The purpose of this review article is to give an up to date account of the theory and
applications of scale functions for spectrally negative Lévy processes. Our review also …

Tempered fractional calculus

F Sabzikar, MM Meerschaert, J Chen - Journal of Computational Physics, 2015‏ - Elsevier
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an
exponential factor leads to tempered fractional derivatives and integrals. Tempered …

Tempered anomalous diffusion in heterogeneous systems

MM Meerschaert, Y Zhang… - Geophysical Research …, 2008‏ - Wiley Online Library
Passive tracers in heterogeneous media experience preasymptotic transport with scale‐
dependent anomalous diffusion, before eventually converging to the asymptotic diffusion …

The fractional Poisson process and the inverse stable subordinator

M Meerschaert, E Nane, P Vellaisamy - 2011‏ - projecteuclid.org
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its
distributions solve a time-fractional analogue of the Kolmogorov forward equation for a …

[HTML][HTML] Tempered stable Lévy motion and transient super-diffusion

B Baeumer, MM Meerschaert - Journal of Computational and Applied …, 2010‏ - Elsevier
The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are
transition densities of a stable Lévy motion, representing the accumulation of power-law …

Analyzing the spectrum of asset returns: Jump and volatility components in high frequency data

Y Aït-Sahalia, J Jacod - Journal of Economic Literature, 2012‏ - aeaweb.org
This paper reports some of the recent developments in the econometric analysis of
semimartingales estimated using high frequency financial returns. It describes a simple yet …

Characterization of dependence of multidimensional Lévy processes using Lévy copulas

J Kallsen, P Tankov - Journal of Multivariate analysis, 2006‏ - Elsevier
This paper suggests Lévy copulas in order to characterize the dependence among
components of multidimensional Lévy processes. This concept parallels the notion of a …

Modelling tail risk with tempered stable distributions: an overview

H Fallahgoul, G Loeper - Annals of Operations Research, 2021‏ - Springer
In this study, we investigate the performance of different parametric models with stable and
tempered stable distributions for capturing the tail behaviour of log-returns (financial asset …

Efficiently sampling nested Archimedean copulas

M Hofert - Computational Statistics & Data Analysis, 2011‏ - Elsevier
Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are
presented. First, efficient sampling algorithms for the nested Archimedean families of Ali …

Tempered fractional Brownian motion

MM Meerschaert, F Sabzikar - Statistics & Probability Letters, 2013‏ - Elsevier
Tempered fractional Brownian motion (TFBM) modifies the power law kernel in the moving
average representation of a fractional Brownian motion, adding an exponential tempering …