The modelling of systems by differential equations usually requires
that the parameters involved be completely known. Such models often
originate from problems in physics or economics where we have
insufficient information on parameter values. One important class
of stochastic mathematical models is stochastic partial
differential equations (SPDEs), which can be seen as deterministic
partial differential equations (PDEs) with finite or infinite
dimensional stochastic processes - either with colour noise or
white noise. Though white noise is a purely mathematical
construction, it can be a good model for rapid random
fluctuations.This research monograph concerns analysis of
discrete-time approximations for stochastic differential equations
(SDEs) driven by Wiener processes. The first chapter of the book
provides a theoretical basis for working with SDEs and stochastic
processes.This book has been written in a simple and clear
mathematical logical language. The basic definitions and theorems
on stochastic calculus have been provided initially. Each chapter
contains illustrated examples via figures and tables. Problems are
included which will help readers understand the theories better.
Also, the reader can construct new wavelets by using the procedure
presented in the book. It will certainly fill up the blank space
that the lack of a comprehensive book has caused.
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