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For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…

Methodology · Statistics 2023-12-25 Simon Nik , Christian H. Weiß

In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…

Probability · Mathematics 2019-01-16 Nicolas Marie

This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…

Probability · Mathematics 2014-03-19 Yaozhong Hu , David Nualart , Qing Zhou

We investigate the existence of densities for finite-dimensional distributions of Hermite processes of order \(q \ge 1\) and self-similarity parameter \(H\in(\frac12,1)\). Whereas the Gaussian case \(q=1\) (fractional Brownian motion) is…

Probability · Mathematics 2025-09-26 Laurent Loosveldt , Yassine Nachit , Ivan Nourdin , Ciprian Tudor

We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…

Probability · Mathematics 2020-10-22 Mikolaj J. Kasprzak

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…

Probability · Mathematics 2019-12-06 Xiliang Fan , Rong Yu

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…

Statistics Theory · Mathematics 2022-11-23 Yury A. Kutoyants

The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this work, we derive the Wiener chaos expansion of this…

Probability · Mathematics 2024-10-23 Gi-Ren Liu , Yuan-Chung Sheu , Hau-Tieng Wu

We prove Gaussian tail estimates for the transition probability of $n$ particles evolving as symmetric exclusion processes on $\bb Z^d$, improving results obtained in \cite{l}. We derive from this result a non-equilibrium Boltzmann-Gibbs…

Probability · Mathematics 2007-05-23 C. Landim

Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…

Statistics Theory · Mathematics 2023-03-28 Didong Li , Wenpin Tang , Sudipto Banerjee

By using the Malliavin calculus and finite jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic (partial) differential equations with noises containing a subordinate…

Probability · Mathematics 2016-01-11 Feng-Yu Wang

In this paper, we provide upper bounds on the d2 distance between a large class of functionals of a multivariate compound Hawkes process and a given Gaussian vector. This is proven using Malliavin's calculus defined on an underlying Poisson…

Probability · Mathematics 2021-09-17 Mahmoud Khabou

The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.

Probability · Mathematics 2010-07-06 S. V. Lototsky , B. L. Rozovskii , D. Seleši

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

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…

Applications · Statistics 2017-10-03 Christos Merkatas , Konstantinos Kaloudis , Spyridon J. Hatjispyros

We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…

Statistics Theory · Mathematics 2020-09-02 Mikkel Bennedsen

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

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Machine Learning · Statistics 2014-04-08 Maurizio Filippone , Mark Girolami

A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…

Machine Learning · Statistics 2014-08-05 Naoki Tanaka , Shohei Shimizu , Takashi Washio

We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian…

Methodology · Statistics 2013-02-14 Y. Pokern , A. M. Stuart , J. H. van Zanten