Related papers: Connection between deriving bridges and radial par…
We propose a novel stochastic method to exactly generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$. These paths are weighted with a probability given by the overdamped…
We consider an Ornstein-Uhlenbeck process with values in R^n driven by a L\'evy process (Z_t) taking values in R^d with d possibly smaller than n. The L\'evy noise can have a degenerate or even vanishing Gaussian component. Under a…
The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional…
Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample…
In the L\'evy construction of Brownian motion, a Haar-derived basis of functions is used to form a finite-dimensional process $W^{N}$ and to define the Wiener process as the almost sure path-wise limit of $W^{N}$ when $N$ tends to infinity.…
Constructing \Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the \emph{a-reminder}…
We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in the Glivencko-Cantelli theorem. Combining a functional…
In this short communication we present a (functional) central limit theorem for the idle process of a one-sided reflected Ornstein-Uhlenbeck proces.
Tverberg's theorem is one of the cornerstones of discrete geometry. It states that, given a set $X$ of at least $(d+1)(r-1)+1$ points in $\mathbb R^d$, one can find a partition $X=X_1\cup \ldots \cup X_r$ of $X$, such that the convex hulls…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
We investigate the concept of cylindrical Wiener process subordinated to a strictly $\alpha$-stable L\'evy process, with $\alpha\in\left(0,1\right)$, in an infinite dimensional, separable Hilbert space, and consider the related stochastic…
We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
We continue the investigation of sample paths of $q$-Ornstein-Uhlenbeck process. We show that for all $q\in(-1,1)$, the process has big jumps crossing from near one end point of the domain to the other with positive probability. Moreover,…
We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads…
In this paper we study the L\'evy Ornstein- Uhlenbeck equation $\partial_t X_t=-m\,X_t+\eta$. The transition kernel of the L\'evy Ornstein- Uhlenbeck process is given by a series which is not convergent in general, a large diffusion…
The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on L\'evy driven Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these processes can be…
Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of…
This is a survey on recent progresses in the study of branching processes with immigration, generalized Ornstein-Uhlenbeck processes and affine Markov processes. We mainly focus on the applications of skew convolution semigroups and the…