Related papers: Rough McKean-Vlasov dynamics for robust ensemble K…
The existence of random dynamical systems for McKean--Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this…
Vehicle state estimation presents a fundamental challenge for autonomous driving systems, requiring both physical interpretability and the ability to capture complex nonlinear behaviors across diverse operating conditions. Traditional…
Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…
We investigate the complexities of the McKean-Vlasov optimal control problem, exploring its various formulations such as the strong and weak formulations, as well as both Markovian and non-Markovian setups within financial markets.…
We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on the coefficients, in agreement with the respective…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…
A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of…
Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…
Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a data-driven mesoscopic modeling framework that combines the kinetic theory of active particles with…
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…
This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…
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,…
Safe navigation is a fundamental challenge in multi-robot systems due to the uncertainty surrounding the future trajectory of the robots that act as obstacles for each other. In this work, we propose a principled data-driven approach where…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…