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Books > Science & Mathematics > Mathematics > General
Exploring Monte Carlo Methods is a basic text that describes the
numerical methods that have come to be known as "Monte Carlo." The
book treats the subject generically through the first eight
chapters and, thus, should be of use to anyone who wants to learn
to use Monte Carlo. The next two chapters focus on applications in
nuclear engineering, which are illustrative of uses in other
fields. Five appendices are included, which provide useful
information on probability distributions, general-purpose Monte
Carlo codes for radiation transport, and other matters. The famous
"Buffon s needle problem" provides a unifying theme as it is
repeatedly used to illustrate many features of Monte Carlo
methods.
This book provides the basic detail necessary to learn how to
apply Monte Carlo methods and thus should be useful as a text book
for undergraduate or graduate courses in numerical methods. It is
written so that interested readers with only an understanding of
calculus and differential equations can learn Monte Carlo on their
own. Coverage of topics such as variance reduction, pseudo-random
number generation, Markov chain Monte Carlo, inverse Monte Carlo,
and linear operator equations will make the book useful even to
experienced Monte Carlo practitioners.
Provides a concise treatment of generic Monte Carlo methods
Proofs for each chapter
Appendixes include Certain mathematical functions; Bose Einstein
functions, Fermi Dirac functions, Watson functions"
This book is devoted to the study of stochastic measures (SMs). An
SM is a sigma-additive in probability random function, defined on a
sigma-algebra of sets. SMs can be generated by the increments of
random processes from many important classes such as
square-integrable martingales and fractional Brownian motion, as
well as alpha-stable processes. SMs include many well-known
stochastic integrators as partial cases.General Stochastic Measures
provides a comprehensive theoretical overview of SMs, including the
basic properties of the integrals of real functions with respect to
SMs. A number of results concerning the Besov regularity of SMs are
presented, along with equations driven by SMs, types of solution
approximation and the averaging principle. Integrals in the Hilbert
space and symmetric integrals of random functions are also
addressed.The results from this book are applicable to a wide range
of stochastic processes, making it a useful reference text for
researchers and postgraduate or postdoctoral students who
specialize in stochastic analysis.
The valuation of the liability structure can be determined by real
options because the shares of a company can be regarded as similar
to the purchase of a financial call option. Therefore, from this
perspective, debt can be viewed as the sale of a financial put
option. As a result, financial analysts are able to establish
different valuations of a company, according to these two financing
methods. Valuation of the Liability Structure by Real Options
explains how the real options method works in conjunction with
traditional methods. This innovative approach is particularly
suited to the valuation of companies in industries where an
underlying asset has high volatility (such as the mining or oil
industries) or where research and development costs are high (for
example, the pharmaceutical industry). Integration of the economic
value of net debt (rather than the accounting value) and
integration of the asset volatility are the main advantages of this
approach.
These materials were developed, in part, by a grant from the
federally-funded Mathematics and Science Partnership through the
Center for STEM Education. Some of the activities were adapted from
the National Council of Teachers of Mathematics Illuminations, the
National Library of Virtual Manipulatives, Hands-On Math Projects
with Real Applications by Judith A. Muschla and Gary R. Muschla,
Learning Math with Calculators: Activities for Grades 3-8 by Len
Sparrow and Paul Swan, and Mathematical Ideas by Charles D. Miller,
Vern E. Heeren and John Hornsby.
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