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We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…

Statistics Theory · Mathematics 2017-01-01 Salima El Kolei , Florian Pelgrin

We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T].…

Statistics Theory · Mathematics 2013-05-17 Romain Guy , Catherine Laredo , Elisabeta Vergu

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2023-07-17 Zachary Bezemek , Konstantinos Spiliopoulos

We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…

Probability · Mathematics 2017-04-05 Amir Dembo , Mykhaylo Shkolnikov , S. R. Srinivasa Varadhan , Ofer Zeitouni

In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to…

Analysis of PDEs · Mathematics 2018-10-11 Hui Huang , Jian-Guo Liu , Jianfeng Lu

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

Probability · Mathematics 2007-05-23 Clive G. Wells

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…

Numerical Analysis · Mathematics 2025-10-21 Jingtao Zhu , Yuying Zhao , Siqing Gan

We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…

Probability · Mathematics 2025-11-05 Marc Hoffmann , Yating Liu

In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs), possibly with a drift term exhibiting super-linear growth…

Numerical Analysis · Mathematics 2023-06-21 Jianhai Bao , Christoph Reisinger , Panpan Ren , Wolfgang Stockinger

In this work, we present a general Milstein-type scheme for McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and Poisson random measure and the associated system of interacting particles where drift,…

Probability · Mathematics 2025-01-08 Sani Biswas , Chaman Kumar , Christoph Reisinger , Verena Schwarz

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…

Methodology · Statistics 2024-11-12 Ajay Jasra , Mohamed Maama , Raul Tempone

The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…

Probability · Mathematics 2022-09-01 Xuda Ye , Zhennan Zhou

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

For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in…

Statistics Theory · Mathematics 2023-07-19 Miljenko Huzak , Snježana Lubura Strunjak , Andreja Vlahek Štrok

We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…

Probability · Mathematics 2019-08-06 Fabio Coppini , Helge Dietert , Giambattista Giacomin

This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the…

Statistics Theory · Mathematics 2024-11-01 Chiara Amorino , Denis Belomestny , Vytautė Pilipauskaitė , Mark Podolskij , Shi-Yuan Zhou

We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel,…

Machine Learning · Computer Science 2019-05-29 Gabriele Abbati , Philippe Wenk , Michael A Osborne , Andreas Krause , Bernhard Schölkopf , Stefan Bauer

In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…

Probability · Mathematics 2021-09-15 Wei Liu , Liming Wu , Chaoen Zhang

For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…

Statistics Theory · Mathematics 2011-11-09 Stefano Iacus , Masayuki Uchida , Nakahiro Yoshida