In this paper we study a subordinate Brownian motion with a Gaussian component and a rather general discontinuous part. The assumption on the subordinator is that its Laplace exponent is a complete Bernstein function with a Lévy density satisfying a certain growth condition near zero. The main...

In this paper, we consider some families of one-dimensional locally infinitely divisible Markov processes {ηtϵ}0≤t≤T with frequent small jumps. For a smooth functional F(x[0,T]) on space D[0,T], the following asymptotic expansions for expectations are proved: as...

We study the density of the supremum of a strictly stable Lévy process. Our first goal is to investigate convergence properties of the series representation for this density, which was established recently by Hubalek and Kuznetsov (2011) [24]. Our second goal is to investigate in more detail...

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k∈Zd, where (εi)i∈Zd are iid random variables...

In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models (X,V) where both the state process X and the volatility process V may have jumps. Our results relate the asymptotic behavior of the characteristic function of XΔ for some Δ0 in a stationary regime to...

We improve, first, a strong invariance principle from Kifer (2013) [10] for nonconventional sums of the form ∑n=1[Nt]F(X(n),X(2n),…,X(ℓn)) (normalized by 1/N) where X(n),n≥0’s is a sufficiently fast mixing vector process with some moment conditions and stationarity properties and F...

In this paper we consider a continuous-time autoregressive moving average (CARMA) process (Yt)t∈R driven by a symmetric α-stable Lévy process with α∈(0,2] sampled at a high-frequency time-grid {0,Δn,2Δn,…,nΔn}, where the observation grid gets finer and the last observation tends to...

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we...

This paper introduces an unified approach to diffusion approximations of signaling networks. This is accomplished by the characterization of a broad class of networks that can be described by a set of quantities which suffer exchanges stochastically in time. We call this class stochastic Petri...

In this paper, we consider Beta(2−α,α) (with 1α2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number...