Related papers: On Exponential Convergence of Random Variables
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…
We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications…
This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…
We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…