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In this thesis, we consider an anisotropic finite-range bond percolation model on Z2. On each horizontal layer {(x,i):x∈Z} for i∈Z, we have edges ⟨(x,i),(y,i)⟩ for 1≤∣x−y∣≤N with $N\in\mathbb{N ...
This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...
True random number generators (TRNGs) allow the generation of true random bit sequences, guaranteeing the unpredictability and perfect balancing of the generated values. TRNGs can be realised from the sampling of quantum phenomena, for instance, the detect ...
Hoboken2021
Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...
If W is the simple random walk on the square lattice Z(2), then W induces a random walk W-G on any spanning subgraph G subset of Z(2) of the lattice as follows: viewing W as a uniformly random infinite word on the alphabet {x, -x, y, -y}, the walk W-G star ...
Mixed logit models with unobserved inter-and intra-individual heterogeneity hierarchically extend standard mixed logit models by allowing tastes to vary randomly both across individuals and across choice situations encountered by the same individual. Recen ...
The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2020
Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by a recent work of ...
The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in ...
In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...
