CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a “random walk” model — a system in which every step is determined by ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a "random walk" model—a system in which every step is determined by a ...

“To swim against the current of human intuition is a difficult task. ... the human mind is built to identify for each event a definite cause and can, therefore, have a hard time accepting the ...

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures. These are not the kinds of objects that concern Scott Sheffield.