Related papers: Stable and tempered stable distributions and proce…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…
We introduce a notion of geometric tempering using exponentially-dampened Mittag-Leffler tempering functions and closely investigate the univariate case. Characteristic exponents and cumulants are calculated, as well as spectral densities.…
Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…
The class of $\alpha$-stable distributions with a wide range of applications in economics, telecommunications, biology, applied, and theoretical physics. This is due to the fact that it possesses both the skewness and heavy tails. Since…
We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f…
We consider a new family of $\R^d$-valued L\'{e}vy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitely (see for instance \cite{cc}, \cite{ckp},…
This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
We develop the first exact and computationally tractable method for simulating from tempered stable distributions in the infinite variation case, which corresponds to $\alpha\in[1,2)$. A small simulation study shows that the approach works…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be…
Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…
We propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations…
Rapidly decreasing tempered stable distributions are useful models for financial applications. However, there has been no exact method for simulation available in the literature. We remedy this by introducing an exact simulation method in…