Related papers: Evolution of statistical averages: an interdiscipl…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…
Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while…
We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…
Utilizing non-concurrent control data (NCC) in the analysis of late-entering arms in platform trials has recently received considerable attention. While incorporating NCC can lead to increased power and lower sample sizes, it might…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amount of details. In the chronological order we present results…
A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME),…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
In randomized experiments with non-compliance scholars have argued that the complier average causal effect (CACE) ought to be the main causal estimand. The literature on inference of the complier average treatment effect (CACE) has focused…
In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the…
This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the…
We study a broad class of high-dimensional mean-field exchange models, encompassing both noisy and singular dynamics, along with their dual processes. This includes a generalized version of the averaging process as well as some…
We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous…