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We propose a new algorithm for approximating the non-asymptotic second moment of the marginal likelihood estimate, or normalizing constant, provided by a particle filter. The computational cost of the new method is $O(M)$ per time step,…

Methodology · Statistics 2016-08-19 Svetoslav Kostov , Nick Whiteley

Considering well localized atom, the mean field theory (MFT) was applied to replace the operators by equivalent expectation values. The Rabi model was reduced to a fourth orders NDE describing atoms position. Solution by the harmonic…

Quantum Physics · Physics 2020-04-22 Ghasem Asadi Cordshooli , Mehdi Mirzaee

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…

Performance · Computer Science 2021-11-03 Sebastian Allmeier , Nicolas Gast

Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…

Statistical Mechanics · Physics 2020-08-26 Dimitra Maoutsa , Sebastian Reich , Manfred Opper

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…

Numerical Analysis · Mathematics 2023-05-30 Qian Guo , Jie He , Lei Li

The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…

Numerical Analysis · Mathematics 2025-09-01 Martín Hernández

We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…

Probability · Mathematics 2013-09-19 François Bolley

We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We…

Statistics Theory · Mathematics 2024-01-11 Hamidreza Maleki Almani , Tommi Sottinen

We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…

Quantum Physics · Physics 2008-12-18 R. D. Gill , S. Massar

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using the statistics of a final…

Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…

Quantum Physics · Physics 2021-09-17 Toshinari Itoko , Rudy Raymond

We propose a fast potential splitting Markov Chain Monte Carlo method which costs $O(1)$ time each step for sampling from equilibrium distributions (Gibbs measures) corresponding to particle systems with singular interacting kernels. We…

Computational Physics · Physics 2020-10-13 Lei Li , Zhenli Xu , Yue Zhao

We investigate propagation of chaos for mean field Markov Decision Process with common noise (CMKV-MDP), and when the optimization is performed over randomized open-loop controls on infinite horizon. We first state a rate of convergence of…

Optimization and Control · Mathematics 2022-07-27 Médéric Motte , Huyên Pham

We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main results are…

Numerical Analysis · Mathematics 2022-12-22 Beniamin Goldys , Chunxi Jiao , Kim-Ngan Le

In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…

Probability · Mathematics 2021-02-19 Jian-Guo Liu , Ziheng Wang , Yantong Xie , Yuan Zhang , Zhennan Zhou

In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…

Probability · Mathematics 2023-06-22 Jian-Guo Liu , Ziheng Wang , Yantong Xie , Yuan Zhang , Zhennan Zhou

We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…

Probability · Mathematics 2023-07-06 Gianmarco Bet , Fabio Coppini , Francesca R. Nardi

We study the rate of convergence w.r.t.~a Wasserstein type distance for random walk approximations of mean field BSDEs. Our method does not use the particle method but instead a freezing technique. We extend results by Briand, Ch. Geiss, S.…

Probability · Mathematics 2025-05-21 Boualem Djehiche , Hannah Geiss , Stefan Geiss , Céline Labart , Jani Nykänen

We study the mean field Schr\"odinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the observation of their initial and final configuration. Its…

Probability · Mathematics 2019-05-08 Julio Backhoff-Veraguas , Giovani Conforti , Ivan Gentil , Christian Léonard

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

Machine Learning · Computer Science 2015-02-23 Pierre Baqué , Jean-Hubert Hours , François Fleuret , Pascal Fua