Probability theory has long provided a rigorous framework for quantifying uncertainty, yet its extension to infinite sets introduces profound conceptual challenges and opportunities. Contemporary ...

This is a preview. Log in through your library . Abstract A noncommutative probability theory is developed in which no boundedness, finiteness, or "tracial" conditions are imposed. The underlying ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...

The paper is concerned with the relationship between various modes of convergence for stochastically monotone sequences of random variables. A necessary and sufficient condition, as well as a ...

Source: Thunder Bay, Canada. Used with permission of Dan Hunt, MD. Coincidences attract our attention because they seem weird, odd, or unlikely. Their improbability stimulates wonder—“what are the ...

PROBABILITY theory is a quaint little piece of mathematics. It is about sets of non-negative numbers that are attached to actual and possible physical events, that sum to 1 and that obey certain rules ...

Forbes contributors publish independent expert analyses and insights. I write about physics, science, academia, and pop culture. The outrage of the moment in my social media circles is over the New ...

To many, the concept of probability feels intuitive. We're used to thinking about the odds of everything from coin flips to election results. Probability has become so integral to everyday life, it's ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

SHENZHEN, China, Sept. 19, 2025 /PRNewswire/ -- MicroCloud Hologram Inc. (NASDAQ: HOLO), ("HOLO" or the "Company"), is a technology service provider. In important fields such as quantum measurement ...