Related papers: Green Measures for a Class of non-Markov Processes
We provide some equations for the Variance Gamma process due to the fact that we do not consider only the definition as a time-changed Brownian motion. This brings us to a new non-local equation, even true in the drifted case, involving…
A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…
In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…
It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…
We consider a branching Brownian motion in $\mathbb{R}^d$. We prove that there exists a random subset $\Theta$ of $\mathbb{S}^{d-1}$ such that the limit of the derivative martingale exists simultaneously for all directions $\theta \in…
Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this…
In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes…
We consider the noncolliding Brownian motion (BM) with $N$ particles starting from the eigenvalue distribution of Gaussian unitary ensemble (GUE) of $N \times N$ Hermitian random matrices with variance $\sigma^2$. We prove that this process…
We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…
Let B_1,B_2, ... be independent one-dimensional Brownian motions defined over the whole real line such that B_i(0)=0. We consider the nth iterated Brownian motion W_n(t)= B_n(B_{n-1}(...(B_2(B_1(t)))...)). Although the sequences of…
In this article we study stability properties of $g_O$, the standard Green kernel for $O$ an open regular set in $R^d$. In $d\ge 3$ we show that $g_O^\beta$ is again a Green kernel of a Markov Feller process, for any power $\beta\in…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
We study the issue of integration with respect to the non-commutative fractional Brownian motion, that is the analog of the standard fractional Brownian in a non-commutative probability setting.When the Hurst index $H$ of the process is…
We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [\alpha_0,2]$ for some $\alpha_0>0$. In addition, we estimate the difference between the heat kernels…
The triangular elliptic operators are natural extensions of the elliptic deformation of circular operators. We obtain a Brown measure formula for the sum of a triangular elliptic operator $g_{_{\alpha, \beta, \gamma}}$ with a random…
We introduce a two-parameter family of diffusion processes $(B_{r,s}^N(t))_{t\ge 0}$, $r,s>0$, on the general linear group $\mathbb{GL}_N$ that are Brownian motions with respect to certain natural metrics on the group. At the same time, we…
This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) for small data in $L^2$ and we show these measures to be absolutely continuous with respect to the…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…
We solve the problem of asymptotic behaviour of the renewal measure (Green function) generated by a transient Lamperti's Markov chain $X_n$ in $\mathbf R$, that is, when the drift of the chain tends to zero at infinity. Under this setting,…