In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The...

We calculate the density function of (U∗(t),θ∗(t)), where U∗(t) is the maximum over [0,g(t)] of a reflected Brownian motion U, where g(t) stands for the last zero of U before t, θ∗(t)=f∗(t)−g∗(t), f∗(t) is the hitting time of the level U∗(t), and g∗(t) is the left-hand...

We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ϵσ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process...

In the early 1990s, Avram and Taqqu showed that regularly varying moving average processes with all coefficients nonnegative and the tail index α strictly between 0 and 2 satisfy the functional limit theorem. They also conjectured that an equivalent statement holds under a certain less...

We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross–Sobolev space D1,2 of random variables with a square-integrable Malliavin derivative, we let ΓF,G≔〈DF,−DL−1G〉, where D is the Malliavin derivative operator and L−1 is the...

In 1983, N. Herrndorf proved that for a ϕ-mixing sequence satisfying the central limit theorem and lim infn→∞σn2/n0, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second moments and a weaker type (α, β, ρ) of mixing the...

A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity properties, we construct a continuous time, measure-valued...

We study a two-dimensional joint distribution related to the first passage time below a level for a continuous-state branching process with immigration. We provide an explicit expression of its Laplace transform and obtain a necessary and sufficient criterion for transience or recurrence. We...

We generalize the BM-local time fractional symmetric α-stable motion introduced in Cohen and Samorodnitsky (2006) by replacing the local time with a general continuous additive functional (CAF). We show that the resulting process is again symmetric α-stable with stationary increments....

This work is devoted to the study of a stochastic variational inequality with a Wiener–Poisson driving term. Existence and uniqueness are proven for Lipschitz coefficients and under general conditions for the unbounded term. One of the main tools used in order to obtain the existence result is...