arXiv subjects

Emanuela Sasso

Publications and source records attributed to Emanuela Sasso.

7 recordsLinked to original sources

arXiv2024

The Spectral Gap of a Gaussian Quantum Markovian Generator

Gaussian quantum Markov semigroups are the natural non-commutative extension of classical Ornstein-Uhlenbeck semigroups. They arise in open quantum systems of bosons where canonical non-commuting random variables of positions and momenta come into play. If there exits a faithful invariant density we explicitly compute the optimal exponential convergence rate, namely the spectral gap of the generator, in non-commutative $L^2$ spaces determined by the invariant density showing that the exact value is the lowest eigenvalue of a certain matrix determined by the diffusion and drift matrices. The spectral gap turns out to depend on the non-commutative $L^2$ space considered, whether the one determined by the so-called GNS or KMS multiplication by the square root of the invariant density. In the first case, it is strictly positive if and only if there is the maximum number of linearly independent noises. While, we exhibit explicit examples in which it is strictly positive only with KMS multiplication. We do not assume any symmetry or quantum detailed balance condition with respect to the invariant density.

math.FA↗

arXiv2022

On non-centered maximal operators related to a non-doubling and non-radial exponential measure

We investigate mapping properties of non-centered Hardy-Littlewood maximal operators related to the exponential measure $d\mu(x) = \exp(-|x_1|-\ldots-|x_d|)dx$ in $\mathbb{R}^d$. The mean values are taken over Euclidean balls or cubes ($\ell^{\infty}$ balls) or diamonds ($\ell^1$ balls). Assuming that $d \ge 2$, in the cases of cubes and diamonds we prove the $L^p$-boundedness for $p > 1$ and disprove the weak type $(1,1)$ estimate. The same is proved in the case of Euclidean balls, under the restriction $d \le 4$ for the positive part.

math.CA↗

arXiv2021

The general structure of the Decoherence-free subalgebra for uniformly continuous Quantum Markov semigroups

By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous QMSs. Moreover we prove that, when there exists a faithful normal invariant state, N(T) has to be atomic and decoherence takes place.

quant-ph↗

arXiv2020

A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and Lévy-driven Ornstein-Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang [23] because it does not rely on an acceptance-rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques

q-fin.CP↗

arXiv2020

Correlating Lévy processes with Self-Decomposability: Applications to Energy Markets

Based on the concept of self-decomposability, we extend some recent multivariate Lévy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related markets after a certain stochastic time delay. Consequently, we study the properties of such processes, derive closed form expressions for the characteristic function and detail how a Monte Carlo scheme can be easily implemented. We illustrate the applicability of our approach in the context of gas and power Energy markets focusing on the calibration and on the pricing of spread options written on different underlying assets using simulations techniques.

q-fin.PR↗

arXiv2016

Structure of Uniformly Continuous Quantum Markov Semigroups

The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a naturaldecomposition of a Markovian open quantum system into its noiseless (decoherence-free) and irreducible (ergodic) components. This leads to a new characterisation of the structure of invariant states and a new method for finding decoherence-free subsystems and subspaces. Examples are presented to illustrate these results.

math-ph↗

arXiv2016

Market forecasting using Hidden Markov Models

Working on the daily closing prices and logreturns, in this paper we deal with the use of Hidden Markov Models (HMMs) to forecast the price of the EUR/USD Futures. The aim of our work is to understand how the HMMs describe different financial time series depending on their structure. Subsequently, we analyse the forecasting methods exposed in the previous literature, putting on evidence their pros and cons.

stat.ML↗