Stochastic processes in the context of "Ulf Grenander"

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other.

When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence, but not the other way around. In the standard literature of probability theory, statistics, and stochastic processes, independence without further qualification usually refers to mutual independence.

Norbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.

Wiener is considered the originator of cybernetics, the science of communication as it relates to living things and machines, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society. His work heavily influenced computer pioneer John von Neumann, information theorist Claude Shannon, anthropologists Margaret Mead and Gregory Bateson, and others.

Andrey Andreyevich Markov (14 June [O.S. 2 June] 1856 – 20 July 1922) was a Russian mathematician celebrated for his pioneering work in stochastic processes. He extended foundational results—such as the law of large numbers and the central limit theorem—to sequences of dependent random variables, laying the groundwork for what would become known as Markov chains. To illustrate his methods, he analyzed the distribution of vowels and consonants in Alexander Pushkin's Eugene Onegin, treating letters purely as abstract categories and stripping away any poetic or semantic content.

He was also a strong chess player.