This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order ...to analyze this class of open quantum systems, we propose a quantum–classical Bayesian inference method based on the definition of a so-called quantum–classical conditional expectation. It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive the fault tolerant quantum filter and the fault detection equation for this class of open quantum systems. An example of two-level open quantum systems subject to Poisson-type faults is presented to illustrate the proposed method. These results have the potential to lead to a new fault tolerant control theory for quantum systems.
Conditional supremum in Riesz spaces and applications Azouzi, Youssef; Ben Amor, Mohamed Amine; Cherif, Dorsaf ...
Journal of mathematical analysis and applications,
03/2024, Letnik:
531, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool is crucial in ...generalizing various results across multiple disciplines to the framework of Riesz spaces. Among other applications, we utilize this concept in finance to derive characterizations of certain financial conditions.
Regression analysis methods, such as linear regression for continuous outcomes and logistic regression for binary outcomes, have been widely used in medical research data analysis for many years. ...However, there have been instances of misconceptions and misinterpretations of regression results within the medical community. Univariate and multiple regression analyses are commonly used by medical publications to identify factors that are significantly correlated with the outcome. In this manuscript, we critically evaluate the validity of this approach. Our findings indicate that this method is invalid and should be completely disregarded by medical researchers.
This paper supplements the previous contribution by Denuit and Robert (2021). First, the compound Poisson case is revisited and the strong law of large number is rigorously established for the ...conditional expectations defining the conditional mean risk allocation. Then, a weak law of large numbers is proposed, providing the actuary with a criterion ensuring that the variance of individual contributions tends to 0. This is appealing for applications since this behavior is a key success factor for collaborative insurance pools.
We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). The ...financial position is given by an RCLL adapted process. We first state some properties of RBSDEs with jumps when the obstacle process is RCLL only. We then prove that the value function of the optimal stopping problem is characterized as the solution of an RBSDE. The existence of optimal stopping times is obtained when the obstacle is left-upper semi-continuous along stopping times. Finally, we investigate robust optimal stopping problems related to the case with model ambiguity and their links with mixed control/optimal stopping game problems. We prove that, under some hypothesis, the value function is equal to the solution of an RBSDE. We then study the existence of saddle points when the obstacle is left-upper semi-continuous along stopping times.
In this paper, the least squares estimator of random variables for a convex operator is investigated on LF∞(μ) space. We adopt much weaker conditions for the convex operator than in Ji et al. (2020) ...and Sun and Ji (2017). These weaker conditions can also guarantee that the minimax theorem holds. Due to Komlós theorem and the minimax theorem, the existence and uniqueness of the least squares estimator are obtained.
Given a real valued functional T on the space of bounded random variables, we investigate the problem of the existence of a conditional version of nonlinear means. We follow a seminal idea by Chisini ...(1929), defining a mean as the solution of a functional equation induced by T. We provide sufficient conditions which guarantee the existence of a (unique) solution of a system of infinitely many functional equations, which will provide the so-called Conditional Chisini mean. We apply our findings in characterizing the scalarization of conditional Risk Measures, an essential tool originally adopted by Detlefsen and Scandolo (2005) to deduce the robust dual representation.
Display omitted
•The non-parametric rPCA-ACE model was proposed to predict the oxygenates in gasoline samples.•Spectral data were subjected to rPCA and the first 6 PC scores were used as input ...variables to the ACE.•ACE was used to identify the optimal transformations of the dependent/independent variables.•The ACE model showed superior performance compared to linear PCR and PLS regression models.
Accurate estimation of oxygenates is a critical issue in the quality evaluation of gasoline samples. This work aims to examine the nonparametric robust principal component analysis-alternating conditional expectation (rPCA-ACE) algorithm combined with FTIR spectroscopy as a rapid and accurate analytical method for predicting the quality of gasoline samples based on oxygenates content (methanol, methyl tert-butyl ether, and isobutanol). In the ACE algorithm, a set of optimal transformations is estimated for both the independent and dependent variables. These transformations reveal their non-linear relationships and generate a maximum linear effect between the transformed independent variables and the transformed response variable. In this study, the ACE algorithm was applied to an empirical gasoline dataset and considered a series of possible transformations of the independent and dependent variables to find the best transformations. Among all possible transformations, the ACE algorithm identified a series of polynomials and a nearly linear transformation as the best transformations for the independent and dependent variables, respectively. The regression statistics for calibration and prediction, including the correlation coefficient (Rcal2 = 0.9692), root mean square error of calibration (RMSEC = 2.8638), and root mean square error of prediction (RMSEP = 4.0498) (%v/v) for oxygenates content, were calculated. The ACE model showed improved regression results compared to the linear PLS model (Rcal2 = 0.9550, RMSEC = 3.9052, RMSEP = 5.1342) and PCR model (Rcal2 = 0.9160, RMSEC = 6.5330, RMSEP = 7.0270). By applying the ACE technique to the synthetic fully non-linear dataset obtained from the equation y′=exp(y) for the response variable, we demonstrated the power of the ACE algorithm in multivariate analysis and its ability to identify the exact functional relationship between independent and dependent variables to solve fully non-linear problems.
We link conditional weak mixing and ergodicity via the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the ...ergodicity of its tensor product with itself or other ergodic systems. Along the way we characterise components of weak order units in the tensor product space in terms of tensor products of components of weak order units.
PDF
