Related papers: Inverse limits and statistical properties for chao…

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…

In the last decade, a large body of literature has been developed to explain the universal features of inequality in terms of income and wealth. By now, it is established that the distributions of income and wealth in various economies show…

We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…

We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…

In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio,…

We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run…

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…

We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…

We bound features of counterfactual choices in the nonparametric random utility model of demand, i.e. if observable choices are repeated cross-sections and one allows for unrestricted, unobserved heterogeneity. In this setting, tight bounds…

We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…

Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic…

We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous…

Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…

We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon $T$ in an incomplete market model, and then study the asymptotic behavior of minimizing probability as $T\to\infty$.…

Inverse statistics in economics is considered. We argue that the natural candidate for such statistics is the investment horizons distribution. This distribution of waiting times needed to achieve a predefined level of return is obtained…