Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

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 ...

Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding ...

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A random variable is a mathematical function that maps outcomes of random experiments to numbers. It can be thought of as the numeric result of operating a non-deterministic mechanism or performing a ...

Theoretical simulation of random processes means carrying out numerical experiments using artificial random variables. The aim of simulation is not to reproduce the behavior of a physical system, but ...

ABSTRACT: It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on ...

ABSTRACT: In this paper we study the solution of random linear oscillatory equation without damping and with random leading condition using the method. Finally, the time evolution of the mean, ...

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