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

For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process.

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 ...

Random walks constitute one of the most fundamental models in the study of stochastic processes, representing systems that evolve in a sequence of random steps. Their applications range from modelling ...

This is a preview. Log in through your library . Abstract We construct a nondecreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the ...

Here’s a game Claude Shannon, the founder of information theory, invented in 1948. He was trying to model the English language as a random process. Go to your bookshelf, pick up a random book, open it ...

In the real world, probability is a tough thing to characterize. If I roll a die, what does it mean to say that it has a one-sixth chance of coming up 5? We say that the outcome is random because we ...

Researchers have gained a new understanding of how the brain processes reward and risk information. A study by neuroscientists Raymundo Báez-Mendoza from the German Primate Center (DPZ)—Leibniz ...