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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

In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…

Numerical Analysis · Mathematics 2022-03-11 Zezhong Zhang , Richard Archibald , Feng Bao

We introduce a reinforcement learning framework for economic design where the interaction between the environment designer and the participants is modeled as a Stackelberg game. In this game, the designer (leader) sets up the rules of the…

Computer Science and Game Theory · Computer Science 2024-07-22 Gianluca Brero , Alon Eden , Darshan Chakrabarti , Matthias Gerstgrasser , Amy Greenwald , Vincent Li , David C. Parkes

Stochastic resetting, where a dynamical process is intermittently returned to a fixed reference state, has emerged as a powerful mechanism for optimizing first-passage properties. Existing theory largely treats static, non-learning…

Machine Learning · Computer Science 2026-03-18 Jello Zhou , Vudtiwat Ngampruetikorn , David J. Schwab

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…

Populations and Evolution · Quantitative Biology 2012-03-13 Simone Pigolotti , Alessandro Flammini , Amos Maritan

We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…

Machine Learning · Computer Science 2014-08-12 Aristide Tossou , Christos Dimitrakakis

We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…

Machine Learning · Statistics 2013-07-16 Aristide C. Y. Tossou , Christos Dimitrakakis

In this paper we consider a class of generalized Kyle-Back strategic insider trading models in which the insider is able to use the dynamic information obtained by observing the instantaneous movement of an underlying asset that is allowed…

Probability · Mathematics 2022-04-29 Jin Ma , Ying Tan

In this paper, we propose a passivity-based methodology for analysis and design of reinforcement learning in multi-agent finite games. Starting from a known exponentially-discounted reinforcement learning scheme, we show that convergence to…

Optimization and Control · Mathematics 2024-10-30 Bolin Gao , Lacra Pavel

Fully cooperative multiagent systems - those in which agents share a joint utility model- is of special interest in AI. A key problem is that of ensuring that the actions of individual agents are coordinated, especially in settings where…

Computer Science and Game Theory · Computer Science 2013-02-18 Craig Boutilier

Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the…

Machine Learning · Computer Science 2021-06-08 Shaojun Ma , Shu Liu , Hongyuan Zha , Haomin Zhou

We present a novel method for solving population density equations (PDEs), where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different…

Biological Physics · Physics 2017-06-28 Yi Ming Lai , Marc de Kamps

McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…

Probability · Mathematics 2025-07-24 Fabio Bugini , Peter K. Friz , Wilhelm Stannat

The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…

Machine Learning · Computer Science 2023-02-17 Nicholas M. Boffi , Eric Vanden-Eijnden

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

The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…

Dynamical Systems · Mathematics 2016-09-16 Peter L. Simon , Eszter Sikolya

We explore how dynamic entry deterrence operates through feedback strategies in markets experiencing stochastic demand fluctuations. The incumbent firm, aware of its own cost structure, can deter a potential competitor by strategically…

Theoretical Economics · Economics 2024-10-22 Mustapha Nyenye Issah

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the…

Probability · Mathematics 2011-12-06 François Bolley , José A. Cañizo , José A. Carrillo

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin