This paper explores the problem of testing statistical hypotheses when the hypotheses are fuzzy and the data are crisp. The authors introduce new definitions for mass (density) probability functions with fuzzy parameters, as well as probabilities of type I and type II errors. They then present and prove a sequential probability ratio test for fuzzy hypotheses based on these new error definitions. ...
2 weeks ago
The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using a...
1 month ago
We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence. Within our framework, we model nonlinear relations by a multivariate polynomial that can be represented by low-rank symmetric tensors (multi-indexed arrays), making a compromise between model g...
1 month ago
The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation wi...
1 month ago
Institution: Department of Probability and Mathematical Statistics, Charles University, 186 75 Prague, Czech Republic
Email:
Yulia V. Kuvaeva-Gudoshnikova,
Yulia V. Kuvaeva-Gudoshnikova
Institution: Department of Finance, Money Circulation and Credit, Ural State University of Economics, 620144 Yekaterinburg, Russia
Email:
Svetlozar T. Rachev
Svetlozar T. Rachev
Institution: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
Email:
We provide two examples of the appearance of heavy-tailed distributions in social sciences applications. Among these distributions are the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable toy models....
1 month ago