Related papers: On Densities for Solutions to Stochastic Fixed Poi…

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood…

This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…

This paper concerns the analysis of random second order linear differential equations. Usually, solving these equations consists of computing the first statistics of the response process, and that task has been an essential goal in the…

In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…

Mean density of lower dimensional random closed sets, as well as the mean boundary density of full dimensional random sets, and their estimation are of great interest in many real applications. Only partial results are available so far in…

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…

Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…

We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…