Related papers: Semimartingale Stochastic Approximation Procedures…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
We discuss a class of Backward Stochastic Differential Equations(BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated…
The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
We consider a family of parallel methods for constrained optimization based on projected gradient descents along individual coordinate directions. In the case of polyhedral feasible sets, local convergence towards a regular solution occurs…
With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, a Gaussian convergence can be…
This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…
We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…
In this paper, we establish non-asymptotic bounds for accuracy of normal approximation for linear two-timescale stochastic approximation (TTSA) algorithms driven by martingale difference or Markov noise. Focusing on both the last iterate…
In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone (10), offers an…
We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa \cite{AL0}. In this article we focus on second order SPDEs of the Allen-Cahn type. After proving existence, uniqueness, and…
Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…