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We address the problem of parameter estimation for degenerate diffusion processes defined via the solution of Stochastic Differential Equations (SDEs) with diffusion matrix that is not full-rank. For this class of hypo-elliptic diffusions…

Statistics Theory · Mathematics 2024-09-04 Yuga Iguchi , Alexandros Beskos

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

We consider general parameter to solution maps $\theta \mapsto \mathcal G(\theta)$ of non-linear partial differential equations and describe an approach based on a Banach space version of the implicit function theorem to verify the gradient…

Statistics Theory · Mathematics 2026-01-16 Aurélien Castre , Richard Nickl

We study the problem of estimating the coefficients of a diffusion (X_t,t\geq 0); the estimation is based on discrete data X_{n\Delta},n=0,1,...,N. The sampling frequency \Delta^{-1} is constant, and asymptotics are taken as the number N of…

Statistics Theory · Mathematics 2007-06-13 Emmanuel Gobet , Marc Hoffmann , Markus Reiss

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…

Probability · Mathematics 2013-03-14 Tomoyuki Ichiba , Mykhaylo Shkolnikov

This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via…

Probability · Mathematics 2019-10-15 Fabienne Comte , Nicolas Marie

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…

Probability · Mathematics 2020-09-28 Daniel Lacker , Kavita Ramanan , Ruoyu Wu

In this paper, we prove a large deviation principle for the empirical measures of a system of weakly interacting diffusion with reflection. We adopt the weak convergence approach. To make this approach work, we show that the sequence of…

Probability · Mathematics 2023-04-04 Ping Cheng , Rong Wei , Tusheng Zhang

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…

Statistical Mechanics · Physics 2008-10-01 E. Agliari , M. Casartelli , A. Vezzani

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang

We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…

Mathematical Physics · Physics 2022-04-11 Paolo Buttà , Franco Flandoli , Michela Ottobre , Boguslaw Zegarlinski

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…

Statistical Finance · Quantitative Finance 2008-12-02 Alessandro De Gregorio , Stefano Maria Iacus

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

Probability · Mathematics 2025-07-15 Francesca Arceci , Francesco Carlo De Vecchi , Daniela Morale , Stefania Ugolini

We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

Analysis of PDEs · Mathematics 2024-10-18 Jose Antonio Carrillo , Shuchen Guo

We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…

Statistics Theory · Mathematics 2018-04-17 Shota Gugushvili , Peter Spreij

Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…

Probability · Mathematics 2025-10-14 Daniela Morale , Leonardo Tarquini , Stefania Ugolini

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

Soft Condensed Matter · Physics 2009-11-11 Thomas Ihle , Erkan Tuzel , Daniel M. Kroll

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

Statistics Theory · Mathematics 2021-09-20 Teppei Ogihara , Mitja Stadje

By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application,…

Probability · Mathematics 2025-06-10 Panpan Ren , Feng-Yu Wang

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically…

Statistical Mechanics · Physics 2009-10-31 Zbigniew Koza