Related papers: A kinetic equation for economic value estimation w…
We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show…
Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However,…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
A characteristic feature of complex systems in general is a tight coupling between their constituent parts. In complex socio-economic systems this kind of behavior leads to self-organization, which may be both desirable (e.g. social…
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging due to unbounded energy growth under self-similar scaling…
This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation…
A recent kinetic approach for Vicsek-like models of active particles is reviewed. The theory is based on an exact Chapman-Kolmogorov equation in phase space. It can handle discrete time dynamics and "exotic" multi-particle interactions. A…
We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the…
We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by communicating with each other in terms of their distance. To…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
We study a dynamical Ising model of agents' opinions (buy or sell) with coupling coefficients reassessed continuously in time according to how past external news (magnetic field) have explained realized market returns. By combining herding,…
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…
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann…
Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…