Littlewood–Paley–Stein functions for non-local Schrödinger operators

Positivity - Motivated by recent works on vertical Littlewood–Paley–Stein functions for symmetric non-local Dirichlet forms and local Schrödinger type operators respectively, we...     

Spurious correlation as an approximation of the mutual information between redundant outputs and an unknown input

Stochastic resonance (SR) is a counterintuitive phenomenon, observed in a wide variety of nonlinear systems, for which the addition of noise of opportune magnitude can improve signal detection. Tuning the noise for maximizing the SR effect is important both for artificial and biological systems. In the case of artificial systems, full exploitation of the SR effect opens the possibility of measuring otherwise unmeasurable signals. In biology, identification of possible SR maximization mechanisms is of great interest for explaining the low-energy high-sensitivity perception capabilities often observed in animals. SR maximization approaches presented in literature use knowledge on the input signal (or stimulus, in the case of living beings), and maximize the mutual information between the input and the output signal. The input signal, however, is unknown in many practical settings. To cope with this problem, this paper introduces an approximation of the input–output mutual information based on the spurious correlation among a set of redundant units. A proof of the approximation, as well as numerical examples of its application are given.     

First-principles studies on the structural and electronic properties of Li-ion battery cathode material CuF2

The 3d transition metal binary compounds have been extensively investigated for a large multi-electron redox capacity through reversible electrochemical reactions. Here, the structural, electronic and magnetic properties of CuF₂ are studied by the first-principles calculations within both the generalized gradient approximation (GGA) and GGA+U frameworks. Our results show that the antiferromagnetic (AFM) configuration of CuF₂ is more stable than the ferromagnetic (FM) one, which is consistent with experiments. The analysis of the electronic density of states (DOS) shows that CuF₂ is a classic Mott–Hubbard insulator with a large d–d type band gap, which is similar to the case of FeF₃. Moreover, small spin polarizations were found on the sites of fluorin ions, which accords with a fluorin-mediated superexchange mechanism for the Cu–Cu magnetic interaction.     

Analysis of membrane permeation from a deposited droplet

Asymptotically valid analyses are outlined for simulating membrane permeation from a shrinking deposited droplet. A previously published analysis for thick membranes is retraced to elucidate the source of its limitations. A thin membrane solution is also developed. While “thick” and “thin” are superficially defined relative to initial droplet size, the approximations introduced in each analysis are shown to depend more subtly upon droplet solubility in the membrane material.     

Coupling methods and exponential ergodicity for two-factor affine processes

In this paper, by invoking the coupling approach, we establish exponential ergodicity under the L¹-Wasserstein distance for two-factor affine processes. The method employed herein is universal in a certain sense so that it is applicable to general two-factor affine processes, which allow that the first component solves a general Cox-Ingersoll-Ross (CIR) process, and that there are interactions in the second component, as well as that the Brownian noises are correlated; and even to some models beyond two-factor processes.     

Game options with gradual exercise and cancellation under proportional transaction costs

ABSTRACT

Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomized) stopping time, rather than instantly at an ordinary stopping time. Allowing gradual exercise and cancellation leads to increased flexibility in hedging, and hence tighter bounds on the option price as compared to the case of instantaneous exercise and cancellation. Algorithmic constructions for the bid and ask prices, and the associated superhedging strategies and optimal mixed stopping times for both exercise and cancellation are developed and illustrated. Probabilistic dual representations for bid and ask prices are also established.     

Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type

Journal of Theoretical Probability - We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely...