Related papers: Partial Stochastic Dominance via Optimal Transport
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the…
The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori…
Mobile wireless network research focuses on scenarios at the extremes of the network connectivity continuum where the probability of all nodes being connected is either close to unity, assuming connected paths between all nodes (mobile ad…