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The purpose of this work is to construct a {\it Brownian motion} with values in simplicial complexes with piecewise differential structure. In order to state and prove the existence of such Brownian motion, we define a family of continuous…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterization. This class of tilings includes Delaunay triangulations…
We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is a function, say $\phi$, of its local time. It…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
Assume that $X$ is a continuous square integrable process with zero mean, defined on some probability space $(\Omega,\mathrm {F},\mathrm {P})$. The classical characterization due to P. L\'{e}vy says that $X$ is a Brownian motion if and only…
It is well known (Donsker's Invariance Principle) that the random walk converges to Brownian motion by scaling. In this paper, we will prove that the scaled local time of the $(1,L)-$random walk converges to that of the Brownian motion. The…
In this paper we study Markov chains with the state space given by the coordinate axes of $\mathbb R^m$, $m \geq 2$, whose step sizes on each positive half-axis are distributed according to a centered probability distribution with variance…
This paper considers two Brownian motions in a situation where one is correlated to the other with a slight delay. We study the problem of estimating the time lag parameter between these Brownian motions from their high-frequency…
We consider an irreducible pair $\mu \leq_c \nu$ of probability measures on $\mathbb{R}^d$ in convex order. In arXiv:2306.11019, Backhoff, Beiglb\"ock, Schachermayer and Tschiderer have shown that the Stretched Brownian Motion from $\mu$ to…
In this paper, we are concerned with the large N limit of linear combinations of the entries of a Brownian motion on the group of N by N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one.…
In this paper we discuss the process convergence of the time dependent fluctuations of linear eigenvalue statistics of random circulant matrices with independent Brownian motion entries, as the dimension of the matrix tends to $\infty $.…
We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the…
We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped…
We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
It is known from Bramson (1983) that the maximum of branching Brownian motion at time $t$ is asymptotically around an explicit function $m_t$, which involves a first ballistic order and a logarithmic correction. In this paper, we give an…
We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to…