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Numerical methods in probability theory can generally be divided into two groups, deterministic and Monte Carlo methods. Deterministic methods are used for numerical expectations of various random variables whenever such methods are efficient from the point of view of the time spent and the complexity of the numerical procedure. It is widely believed that Monte Carlo methods are used exclusively as an alternative numerical procedure for the numerical estimation of the expectation of random variables. At the same time, it is considered that Monte Carlo methods should be used when they are more efficient than deterministic ones. However, there are numerical procedures in which Monte Carlo methods are an indispensable tool. It is enough to mention statistical models in technical, natural and social sciences, and the bootstrap method for estimating the parameters of a statistical model. Therefore, Monte Carlo methods must be seen as an essential tool in the numerical procedures of probability theory, and should be known as an integral part of probability theory.
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Monte Carlo Simulations Of Random Variables, Sequences And Processes
9 September, 2009, Element d.o.o., Zagreb, Croatia
Paperback
in English
- First edition
9531975698 9789531975698
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Book Details
First Sentence
"To simulate a random variable means to construct its numerical sample of an arbitrary large length."
Table of Contents
Edition Notes
Original book title ' Monte Carlo simulacije slučajnih veličina, nizova i procesa ' written in Croatian.
Isbn (Original Book) : 9789531975629, 9531975620. The Croatian version was published in 2002.
Bibliographical Notes and Bibliography are given at page 299 of the English Translation. Contains index.
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Work Description
The main goal of analysis in this book are Monte Carlo simulations of Markov processes such as Markov chains (discrete time), Markov jump processes (discrete state space, homogeneous and non-homogeneous), Brownian motion with drift and generalized diffusion with drift (associated to the differential operator of Reynolds equation). Most of these processes can be simulated by using their representations in terms of sequences of independent random variables such as uniformly distributed, exponential and normal variables. There is no available representation of this type of generalized diffusion in spaces of the dimension larger than 1. A convergent class of Monte Carlo methods is described in details for generalized diffusion in the two-dimensional space.
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Feedback?December 3, 2023 | Edited by Kaustubh Chakraborty | Added new book |
December 3, 2023 | Created by Kaustubh Chakraborty | Added new book. |