相关论文: Bridge Simulation and Metric Estimation on Lie Gro…
In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this…
In this paper, using an algorithm based on the retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps,…
We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). We provide two algorithms for computing it, using…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional L\'evy random bridge over a random point field, our framework relates the…
Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random…
In this article, we construct samples of SLE-like curves out of samples of CLE and Poisson point process of Brownian excursions. We show that the law of these curves depends continuously on the intensity measure of the Brownian excursions.…
We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed to calculate steady state probabilities of order…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…
In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…
Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by…
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the…
In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018)) established that the distribution of the first hitting times for a diffusing particle subject to hitting an absorber is independent of the direction of the external…
Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the…
Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium steady state depends on the initial condition.…
We study the problem of stopping an $\alpha$-Brownian bridge as close as possible to its global maximum. This extends earlier results found for the Brownian bridge (the case $\alpha=1$). The exact behavior for $\alpha$ close to $0$ is…
A synthetic study of Pitman's and L\'evy's theorems for one-dimensional Brownian bridges with arbitrary endpoints is provided.