相关论文: Limit Theorems for Individual-Based Models in Econ…

The stochastic optimal control of many agents is an important problem in various fields. We investigate the problem of partial observations, where the state of each agent is not fully observed and the control must be decided based on noisy…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

We investigate the fluctuations of the stochastic Becker-D\"oring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a…

We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning…

In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be…

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for…

Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists…

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for…

A general information equilibrium model in the case of ideal information transfer is defined and then used to derive the relationship between supply (information destination) and demand (information source) with the price as the detector of…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

The paper gives picture of enrichment to economic and financial system analysis using agent-based models as a form of advanced study for financial economic data post-statistical-data analysis and micro-simulation analysis. Theoretical…

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this…

In this paper, we briefly discuss a mathematical concept that can be used in economics.

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

The central limit theorem is, with the strong law of large numbers, one of the two fundamental limit theorems in probability theory. Benjamin Jourdain and Alvin Tse have extended to non-linear functionals of the empirical measure of…

One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…