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 ...

Sample space, Field and Probability Measure. Axiomatic definition of Probability. Bayes' theorem. Repeated trials. Continuous and discrete random variables and their probability distribution and ...

Introduction to probability, random processes and basic statistical methods to address the random nature of signals and systems that engineers analyze, characterize and apply in their designs. It ...

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

Random fields and Gaussian processes constitute fundamental frameworks in modern probability theory and spatial statistics, providing robust tools for modelling complex dependencies over space and ...

Journal of Applied Probability and Advances in Applied Probability have for four decades provided a forum for original research and reviews in applied probability, mapping the development of ...

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 ...

Stochastic dynamical systems arise in many scientific fields, such as asset prices in financial markets, neural activity in ...

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