Related papers: Central limit theorem for a Stratonovich integral …
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
By using Malliavin calculus and multiple Wiener-It\^o integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian…
On any denumerable product of probability spaces, we extend the discrete Malliavin structure for conditionally independent random variables. As a consequence, we obtain the chaos decomposition for functionals of conditionally independent…
Given $\{W^{(m)}(t), t \in [0,T]\}_{m \ge 1}$ a sequence of approximations to a standard Brownian motion $W$ in $[0,T]$ such that $W^{(m)}(t)$ converges almost surely to $W(t)$ we show that, under regular conditions on the approximations,…
In this paper, we combine Hida distribution theory and Sobolev-Watanabe-Kree spaces in order to study finely the link between forward integrals obtained by regularization and Wick-It\^o integrals with respect to fractional Brownian motion…
We establish a central limit theorem for partial sums of stationary linear random fields with dependent innovations, and an invariance principle for anisotropic fractional Brownian sheets. Our result is a generalization of the invariance…
We extend our recent result [Cipolloni, Erd\H{o}s, Schr\"oder 2019] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices $X$ with independent, identically distributed complex entries to the real…
We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n-1}subsetmathbb{R}^{n}$ and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
We consider sequences of random variables of the type $S_n= n^{-1/2} \sum_{k=1}^n \{f(X_k)-\E[f(X_k)]\}$, $n\geq 1$, where $X=(X_k)_{k\in \Z}$ is a $d$-dimensional Gaussian process and $f: \R^d \rightarrow \R$ is a measurable function. It…
We consider shot-noise processes with an impulse response written in terms of the logarithm of the ratio between current and event time (instead of the usual absolute time difference). We study its finite-time properties as well as its weak…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…
The process $(G_t)_{t\in[0,T]}$ is referred to as a fractional Gaussian process if the first-order partial derivative of the difference between its covariance function and that of the fractional Brownian motion $(B^H_t)_{t\in[0,T ]}$ is a…
Given a Gaussian process $X$, its canonical geometric rough path lift $\mathbf{X}$, and a solution $Y$ to the rough differential equation (RDE) $\mathrm{d}Y_{t} = V\left (Y_{t}\right ) \circ \mathrm{d} \mathbf{X}_t$, we present a…
A $U$-statistic of a Poisson point process is defined as the sum $\sum f(x_1,\ldots,x_k)$ over all (possibly infinitely many) $k$-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-It\^{o} chaos…
We lay the theoretical and mathematical foundations of the square root of Browniam motion and we prove the existence of such a process. In doing so, we consider Brownian motion on quantized noncommutative Riemannian manifolds and show how a…
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered eigenvalues of $M_n$. Under the…
In this paper, we provide upper bounds on the d2 distance between a large class of functionals of a multivariate compound Hawkes process and a given Gaussian vector. This is proven using Malliavin's calculus defined on an underlying Poisson…