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We extend the L\'evy Langevin Monte Carlo method studied by Oechsler in 2024 to the setting of a target distribution with heavy tails: Choosing a target distribution from the class of subexponential distributions we prove convergence of a…

Probability · Mathematics 2025-07-15 Anita Behme , Claudius Lütke Schwienhorst

We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…

Probability · Mathematics 2021-04-06 Andi Q. Wang , Murray Pollock , Gareth O. Roberts , David Steinsaltz

We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic…

Probability · Mathematics 2012-12-12 Noufel Frikha , Stephane Menozzi

We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…

Computation · Statistics 2023-11-07 Ruiyang Jin , Sumeetpal S. Singh , Nicolas Chopin

Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…

Computation · Statistics 2025-04-28 Shenggang Hu , Hongsheng Dai , Fanlin Meng , Louis Aslett , Murray Pollock , Gareth O. Roberts

We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…

Probability · Mathematics 2025-07-21 Simon Gabriel

We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…

Probability · Mathematics 2020-05-15 Friedrich Götze , Holger Sambale , Arthur Sinulis

We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the…

Numerical Analysis · Mathematics 2022-04-15 Assyr Abdulle , Grigorios A. Pavliotis , Andrea Zanoni

We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…

Analysis of PDEs · Mathematics 2020-08-13 Ivan C. Christov , Akif Ibraguimov , Rahnuma Islam

Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assumptions, we prove that radial solutions of the evolution…

Analysis of PDEs · Mathematics 2021-12-15 Jose A. Carrillo , David Gómez-Castro , Juan Luis Vázquez

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…

Statistics Theory · Mathematics 2025-01-29 Dmytro Marushkevych , Francisco Pina , Mark Podolskij

We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…

Probability · Mathematics 2007-05-23 Alexey M. Kulik

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…

Statistics Theory · Mathematics 2013-08-14 Chenxu Li

In this note we prove the strong Feller property of a strong Markov quasi diffusion process corresponding to an elliptic operator with merely bounded measurable coefficients. We also prove H\"older continuity of harmonic functions…

Probability · Mathematics 2020-01-28 Timur Yastrzhembskiy

In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…

Probability · Mathematics 2022-06-07 Wei Hong , Shihu Li , Xiaobin Sun

We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain $\mathcal D\subset \mathbb R^d$, with Besov-tree random coefficients. This is to say that the logarithms of the diffusion…

Numerical Analysis · Mathematics 2023-02-02 Christoph Schwab , Andreas Stein

We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and use a new formula for the density of a random variable…

Probability · Mathematics 2008-08-18 Ivan Nourdin , Frederi G. Viens

Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment…

Probability · Mathematics 2022-03-17 Anna Gusakova , Holger Sambale , Christoph Thaele

We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…

Probability · Mathematics 2025-10-29 Alessandra Faggionato , Ivailo Hartarsky

In this paper we focus on strong solutions of some heat-like problems with a non-local derivative in time induced by a Bernstein function and an elliptic operator given by the generator or the Fokker-Planck operator of a Pearson diffusion.…

Probability · Mathematics 2021-06-30 Giacomo Ascione , Nikolai Leonenko , Enrica Pirozzi