Related papers: First-Passage Time: A Conception Leading to Supers…
The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
It is often necessary to compare the power spectra of two or more time series: one may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
This paper introduces a new way to compact a continuous probability distribution $F$ into a set of representative points called support points. These points are obtained by minimizing the energy distance, a statistical potential measure…
First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time dependent force, we study the subdiffusion…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and…