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 ...

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 ...

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

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

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion.

In this study, we establish the Marcinkiewicz–Zygmund strong law of large numbers for randomly weighted sums of negatively orthant dependent random variables. The law of the single law of logarithm ...

A newly discovered set of mathematical equations describes how to turn any sequence of random events into a clock, scientists ...

There is a growing sense among physicists that all physical processes can be thought of in terms of the information they store and process; by some accounts information is the basic unit of existence ...