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The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely understood. This paper studies the superiority of symplectic…

Numerical Analysis · Mathematics 2025-05-29 Jialin Hong , Ge Liang , Derui Sheng

We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known…

Statistics Theory · Mathematics 2014-06-24 Valentine Genon-Catalot , Catherine Larédo

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…

Statistics Theory · Mathematics 2020-12-01 Laura Dumitrescu , Ioana Schiopu-Kratina

The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…

Optimization and Control · Mathematics 2012-08-07 Soummya Kar , Jose' M. F. Moura , H. Vincent Poor

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…

chao-dyn · Physics 2008-02-03 J. Bricmont , A. Kupiainen , G. Lin

In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider…

Probability · Mathematics 2019-02-22 Guang Lin , Yanghui Liu , Samy Tindel

We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in $V$-norm, path-wise along almost all observation sequences. In contrast to previous works, our results allow for unbounded…

Computation · Statistics 2015-12-16 Mathieu Gerber , Nick Whiteley

This survey paper is written with the intention of giving a mathematical introduction to filtering techniques for intermittent data assimilation, and to survey some recent advances in the field. The paper is divided into three parts. The…

Numerical Analysis · Mathematics 2012-09-03 Colin J. Cotter , Sebastian Reich

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

Statistics Theory · Mathematics 2022-07-04 Teppei Ogihara

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Optimization and Control · Mathematics 2019-10-18 Romeo Ortega , Vladislav Gromov , Emmanuel Nuño , Anton Pyrkin , Jose Guadalupe Romero

We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…

Dynamical Systems · Mathematics 2014-12-03 Tyrus Berry , John Harlim

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…

Statistics Theory · Mathematics 2020-07-27 Emil S. Jørgensen , Michael Sørensen

In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…

Numerical Analysis · Mathematics 2025-12-04 Chuchu Chen , Xinyu Chen , Jialin Hong , Yuqian Miao

A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…

History and Overview · Mathematics 2024-04-08 Michaël Bensimhoun

This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…

Optimization and Control · Mathematics 2022-10-19 Anugu Sumith Reddy , Amit Apte

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a…

Functional Analysis · Mathematics 2019-02-14 Lassi Paunonen , David Seifert

A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…

Classical Analysis and ODEs · Mathematics 2019-03-27 Dhurjati Prasad Datta , Soma Sarkar

This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Ming Li , Fan Liu , Yifeng Xiong , Jie Xu , Tao Liu

As saturated output observations are ubiquitous in practice, identifying stochastic systems with such nonlinear observations is a fundamental problem across various fields. This paper investigates the asymptotically efficient identification…

Machine Learning · Computer Science 2025-04-07 Lantian Zhang , Lei Guo

We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on…

Numerical Analysis · Mathematics 2026-04-02 Paweł Przybyłowicz , Martyna Wiącek