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 ...

Stochastic processes as a research area focuses on the mathematical modeling and analysis of systems that evolve randomly over time, typically formalized as families of random variables indexed by ...

ABSTRACT: Repeated convolution and truncation of a truncated fat-tailed distribution, instead of Monte Carlo simulation, for pricing a discrete, simple barrier option is presented. The parameters for ...

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 ...

Accurately predicting the remaining mechanical equipment is of great significance for ensuring the safe operation of the equipment and improving economic efficiency. To accurately assess the ...

Abstract: This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily ...

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 ...

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the ...