Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their...

The distribution of the excess process describing heights of extreme values can be approximated by the distribution of a Poisson cluster process. An estimate of the accuracy of such an approximation has been derived in [4] in terms of the Wasserstein distance. The paper presents a sharper...

Abstract: We inscribe Stein's density approach for discrete distributionsin a new, exible framework, hereby extending and unifying a large portionof the relevant literature.We use this to derive a Stein identity whose powerwe illustrate by obtaining a wide variety of so-called inequalities...

We inscribe Stein's density approach for discrete distributions in a new, flexible framework, hereby extending and unifying a large portion of the relevant literature. We use this to derive a Stein identity whose power we illustrate by obtaining a wide variety of so-called inequalities between...

Considering the Markov binomial distribution we investigate its convergence to the limiting Poisson law. Two analogues of the Johnson-Simons theorem are obtained.

We consider the contour representation of the infinite volume Ising model at any fixed inverse temperature ββ∗, the solution of ∑θ:θ∋0e−β|θ|=1. Let μ be the infinite-volume “+” measure. Fix V⊂Zd, λ0 and a (large) N such that calling GN,V the set of contours of length at...

To compute the distribution of the downtime in a time interval [0,t] for a highly available monotone system, a Compound Poisson process (CP(t)) approximation is often used. In this paper we give sufficient conditions for when the distribution ofCP(t) is an asymptotic limit. We also study the...

To compute the distribution of the downtime in a time interval [0,t] for a highly available monotone system, a Compound Poisson process (CP(t)) approximation is often used. In this paper we give sufficient conditions for when the distribution ofCP(t) is an asymptotic limit. We also study the...