Related papers: Star-Shaped deviations
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…
Differential rotation is central to a great many mysteries in stars and planets. In Part I we predicted the order of magnitude and scaling of the differential rotation in both hydrodynamic and magnetohydrodynamic convection zones. Our…
Most galaxies have a warped shape when they are seen from an edge-on point of view. The reason for this curious form is not completely known so far and in this work we apply dynamical system tools to contribute to its explanation. Starting…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent…
Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the…
Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…
We present a detailed study of the small frequency separations as diagnostics of the mass of the convective core and evolutionary stage of solar-type stars. We demonstrate how the small separations can be combined to provide sensitive tests…
We propose a new class of measures for shaping time-dependent trajectories in dynamic optimization (DO). The proposed measures are analogous to risk measures used in stochastic optimization (SO) and are inspired by a recently-proposed…
We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…
In previous work we identified six Sun-like stars observed by Kepler with exceptionally clear asteroseismic signatures of rotation. Here, we show that five of these stars exhibit surface variability suitable for measuring rotation. In order…
Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…
This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible…
The photometric properties of the variable stars located in the lower part of the classical instability strip are discussed. The importance of the determination of some light curve parameters and their connection with the stellar models are…
In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…