In a new SSRN paper, the Abu Dhabi-based quant researcher traces the equations behind modern option pricing back to their ...

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

Will a certain tritium atom decay by a certain time? According to our current science, this question concerning physical phenomena should be answered by sampling from a probability distribution, a ...

An essential companion for advanced undergraduate and graduate level courses in probability, this book describes the tools and results that are used extensively in the field and has worked examples, ...

Probability inequalities provide bounds on the likelihood that a stochastic process deviates from its expected behaviour. They encompass a broad class of results—such as exponential, sub-Gaussian and ...

Branching processes in random environments (BPREs) extend classical Galton–Watson models by allowing the reproduction law to vary according to a sequence of random factors. In each generation, the ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

Models for random message signals and noise encountered in communication systems are developed in this chapter. Random signals cannot be explicitly described prior to their occurrence, and noises ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...

CATALOG DESCRIPTION: Advanced topics in random processes: point processes, Wiener processes; Markov processes, spectral representation, series expansion of random processes, linear filtering, Wiener ...