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Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

Machine Learning · Computer Science 2024-04-02 Hanlin Yu , Marcelo Hartmann , Bernardo Williams , Arto Klami

We take into consideration generalization bounds for the problem of the estimation of the drift component for ergodic stochastic differential equations, when the estimator is a ReLU neural network and the estimation is non-parametric with…

Statistics Theory · Mathematics 2025-06-02 Simone Di Gregorio , Francesco Iafrate

We study inference for the driving L\'evy noise of an ergodic stochastic differential equation (SDE) model, when the process is observed at high-frequency and long time and when the drift and scale coefficients contain finite-dimensional…

Methodology · Statistics 2022-03-22 Hiroki Masuda , Lorenzo Mercuri , Yuma Uehara

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

Machine Learning · Statistics 2019-02-13 Lea Duncker , Gergo Bohner , Julien Boussard , Maneesh Sahani

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…

Statistics Theory · Mathematics 2023-03-21 Hiroki Nemoto , Yasutaka Shimizu

In this paper, we consider possibly misspecified stochastic differential equation models driven by L\'{e}vy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown…

Statistics Theory · Mathematics 2021-10-11 Yuma Uehara

Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade,…

Probability · Mathematics 2021-02-16 Ehsan Azmoodeh , Giovanni Peccati , Xiaochuan Yang

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Applications · Statistics 2013-01-14 Shan Ba , V. Roshan Joseph

We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is…

Statistics Theory · Mathematics 2023-03-09 Daniel Moss , Judith Rousseau

Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…

Probability · Mathematics 2025-09-16 Ranieri Dugo , Giacomo Giorgio , Paolo Pigato

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

Methodology · Statistics 2025-05-06 Martin Bladt , Jorge González Cázares

In this paper we study the problem of semiparametric estimation for a class of McKean-Vlasov stochastic differential equations. Our aim is to estimate the drift coefficient of a MV-SDE based on observations of the corresponding particle…

Statistics Theory · Mathematics 2021-07-02 Denis Belomestny , Vytautė Pilipauskaitė , Mark Podolskij

The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper…

Computational Engineering, Finance, and Science · Computer Science 2025-03-26 Vahab Narouie , Henning Wessels , Fehmi Cirak , Ulrich Römer

We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.

Probability · Mathematics 2015-10-28 Alen Alexanderian

Kruse and Wu [Math. Comp. 88 (2019) 2793--2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and showed that this method attains a temporal…

Numerical Analysis · Mathematics 2026-02-12 Xiao Qi , Yue Wu , Yubin Yan

For a class of piecewise deterministic Markov processes we introduce a stochastic calculus which is a certain non-Gaussian counterpart to the classical Malliavin calculus. As an application we investigate the regularity of densities of…

Probability · Mathematics 2023-06-21 Jörg-Uwe Löbus

A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…

Biological Physics · Physics 2012-09-28 Jun Ohkubo

In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilvel problems, when neither the upper/lower objective values, nor their unbiased gradient estimates are available. In particular, exploiting…

Optimization and Control · Mathematics 2024-04-02 Alireza Aghasi , Saeed Ghadimi

We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…

Statistics Theory · Mathematics 2023-10-18 Denis Belomestny , Shota Gugushvili , Moritz Schauer , Peter Spreij

In this paper, we describe an explicit extension formula in sensitivity analysis regarding the Malliavin weight for jump-diffusion mean-field stochastic differential equations whose local Lipschitz drift coefficients are influenced by the…

Probability · Mathematics 2025-02-04 Samaneh Sojudi , Mahdieh Tahmasebi