From 985d60b29d3139e84ee7a3c2a5747e75417b5c2c Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Tue, 10 Jun 2008 13:20:01 +0000
Subject: new latex package proba (5jun08)

git-svn-id: svn://tug.org/texlive/trunk@8640 c570f23f-e606-0410-a88d-b1316a301751
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 Master/texmf-dist/source/latex/proba/proba.dtx | 256 +++++++++++++++++++++++++
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+% \iffalse meta-comment
+%
+% Copyright 2003 Laurent Nguyen-Ngoc
+%
+% \fi
+%
+% \iffalse
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{proba}
+%<package>     [2003/05/31 The Probability package]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\GetFileInfo{proba.sty}
+\title{The \textsf{proba} package\thanks{Version \fileversion}}
+\author{Laurent Nguyen-Ngoc}
+\date{\filedate}
+\begin{document}
+\maketitle
+\DocInput{proba.dtx}
+\RecordChanges
+\PrintChanges
+\end{document}
+%</driver>
+%
+%\fi
+%
+% \CheckSum{230}
+% \changes{1.0}{2003/05/31}{Initial version}
+% \changes{1.01}{2003/07/26}{Added indicator function}
+% \section{Introduction}
+%
+% The |proba| package provides some shortcuts to mathematical symbols 
+% commonly used when writing articles about probability theory. You should 
+% be aware that some of those shortcuts may intersect with other package 
+% commands, or worse attempt to redefine commands defined elsewhere.
+%
+% In fact, I have not tried to really look at the number of packages that 
+% already exist.
+%
+% The shortcuts are defined with some default symbols associated to them, 
+% but can easily be customized. In fact, it happens quite often that one 
+% needs the same sort of symbol, just with a different letter, in the same 
+% document, and the shortcuts are defined in such a way to accomodate with 
+% this need.
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+% In this section we shall describe the syntax of the commands, as well as 
+% the implementation.
+%
+% \subsection{Sets}
+%
+% We define the set symbols as blackboard letters as provided by the 
+% |amsfonts| package. For those symbols as well as for others, the 
+% |amsfonts| package is therefore required.
+%    \begin{macrocode}
+\RequirePackage{amsfonts}
+%    \end{macrocode}
+% The usual syntax to obtain a set name is |\<Capital Letter>|. More 
+% precisely:
+%    \begin{macrocode}
+\DeclareRobustCommand{\A}[0]{\mathbb{A}}
+\DeclareRobustCommand{\B}[0]{\mathbb{B}}
+\DeclareRobustCommand{\C}[0]{\mathbb{C}}
+\DeclareRobustCommand{\D}[0]{\mathbb{D}}
+\DeclareRobustCommand{\E}[0]{\mathbb{E}}
+\DeclareRobustCommand{\F}[0]{\mathbb{F}}
+\DeclareRobustCommand{\G}[0]{\mathbb{G}}
+\DeclareRobustCommand{\H}[0]{\mathbb{H}}
+\DeclareRobustCommand{\I}[0]{\mathbb{I}}
+\DeclareRobustCommand{\J}[0]{\mathbb{J}}
+\DeclareRobustCommand{\K}[0]{\mathbb{K}}
+\DeclareRobustCommand{\L}[0]{\mathbb{L}}
+\DeclareRobustCommand{\M}[0]{\mathbb{M}}
+\DeclareRobustCommand{\N}[0]{\mathbb{N}}
+\DeclareRobustCommand{\O}[0]{\mathbb{O}}
+\DeclareRobustCommand{\P}[0]{\mathbb{P}}
+\DeclareRobustCommand{\Q}[0]{\mathbb{Q}}
+\DeclareRobustCommand{\R}[0]{\mathbb{R}}
+\DeclareRobustCommand{\S}[0]{\mathbb{S}}
+\DeclareRobustCommand{\T}[0]{\mathbb{T}}
+\DeclareRobustCommand{\U}[0]{\mathbb{U}}
+\DeclareRobustCommand{\V}[0]{\mathbb{V}}
+\DeclareRobustCommand{\W}[0]{\mathbb{W}}
+\DeclareRobustCommand{\X}[0]{\mathbb{X}}
+\DeclareRobustCommand{\Y}[0]{\mathbb{Y}}
+\DeclareRobustCommand{\Z}[0]{\mathbb{Z}}
+%    \end{macrocode}
+% Note that the |\mathbb| command ensures that those shortcuts to sets
+% can be used in math mode only.
+%
+% \subsection{$\sigma$-fields and filtrations}
+%
+% In probability, the $\sigma$-fields and filtrations are commonly
+% designated by letters in calligraphic style. Since such symbols are often
+% needed in a probability-related document, we provide shortcuts to them.
+% The usual syntax in this case is |\cal<Capital Letter>|.
+%    \begin{macrocode}
+\DeclareRobustCommand{\calA}[0]{{\mathcal A}}
+\DeclareRobustCommand{\calB}[0]{{\mathcal B}}
+\DeclareRobustCommand{\calC}[0]{{\mathcal C}}
+\DeclareRobustCommand{\calD}[0]{{\mathcal D}}
+\DeclareRobustCommand{\calE}[0]{{\mathcal E}}
+\DeclareRobustCommand{\calF}[0]{{\mathcal F}}
+\DeclareRobustCommand{\calG}[0]{{\mathcal G}}
+\DeclareRobustCommand{\calH}[0]{{\mathcal H}}
+\DeclareRobustCommand{\calI}[0]{{\mathcal I}}
+\DeclareRobustCommand{\calJ}[0]{{\mathcal J}}
+\DeclareRobustCommand{\calK}[0]{{\mathcal K}}
+\DeclareRobustCommand{\calL}[0]{{\mathcal L}}
+\DeclareRobustCommand{\calM}[0]{{\mathcal M}}
+\DeclareRobustCommand{\calN}[0]{{\mathcal N}}
+\DeclareRobustCommand{\calO}[0]{{\mathcal O}}
+\DeclareRobustCommand{\calP}[0]{{\mathcal P}}
+\DeclareRobustCommand{\calQ}[0]{{\mathcal Q}}
+\DeclareRobustCommand{\calR}[0]{{\mathcal R}}
+\DeclareRobustCommand{\calS}[0]{{\mathcal S}}
+\DeclareRobustCommand{\calT}[0]{{\mathcal T}}
+\DeclareRobustCommand{\calU}[0]{{\mathcal U}}
+\DeclareRobustCommand{\calV}[0]{{\mathcal V}}
+\DeclareRobustCommand{\calW}[0]{{\mathcal W}}
+\DeclareRobustCommand{\calX}[0]{{\mathcal X}}
+\DeclareRobustCommand{\calY}[0]{{\mathcal Y}}
+\DeclareRobustCommand{\calZ}[0]{{\mathcal Z}}
+%    \end{macrocode}
+%
+% \subsection{Probability symbols}
+%
+% Now we deal with symbols more directly related to probability.
+% Probability laws and expectations are often denoted by blackboard
+% letters. Although shortcuts to such letters have already been defined
+% in the set shortcuts, new ones are introduced that also handle 
+% any delimiters needed.
+%
+% \subsubsection{Elementary probability}
+% First some shortcuts to symbols that are used at all levels of 
+% probability theory.
+%
+% \begin{macro}{\prob}
+% First we define a simple |\prob| shortcut that simply produces a 
+% blackboard capital P by default, but whose optional argument makes it 
+% easy to switch to a different letter.
+%    \begin{macrocode}
+\DeclareRobustCommand{\prob}[1][P]{\ensuremath {\mathbb{#1}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\probX}
+% Our next command defines a proability and takes as an argument the event 
+% in the probability. Again, P is the default probability symbol, but any 
+% letter can override it as an optional argument.
+%    \begin{macrocode}
+\DeclareRobustCommand{\probX}[2][{\mathbb{P}}]{\ensuremath{ {#1}\left[ {#2} \right]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\cprobX}
+% |\cprobX| offers a shortcut to type conditional probability. It takes 3 
+% arguments: the first one is the symbol to be used as the probability, 
+% the second one is the event and the last one is the conditioning.
+%    \begin{macrocode}
+\DeclareRobustCommand{\probCX}[3][{\mathbb{P}}]{\ensuremath{ {#1}\left[ {#2} \big| {#3} \right]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\EX}
+% Now are defined the expectation related symbols. We begin by a simple 
+% expectation that takes care of delimiters.
+%    \begin{macrocode}
+\DeclareRobustCommand{\EX}[2][{\mathbb{E}}]{\ensuremath {#1}\left[ {#2} \right]}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\cEX}
+% Just like for probabilities, a conditional version of the expectation is 
+% provided.
+%    \begin{macrocode}
+\DeclareRobustCommand{\cEX}[3][{\mathbb{E}}]{\ensuremath {#1}\left[ {#2} \big| {#3} \right]}
+%    \end{macrocode}
+% \end{macro}
+%
+%�\begin{macro}{\Var}
+% Also a math operator is defined for the variance. 
+% This simple version has just an optional argument that goes as a 
+% subscript to ``Var''.
+%    \begin{macrocode}
+\DeclareRobustCommand{\Var}[1][]{\ensuremath{\mathrm{Var[#1]}}}
+%    \end{macrocode}
+% \end{macro}
+%
+%�\begin{macro}{\VarX}
+% Now we take care of delimiters for what is inside the variance.
+%    \begin{macrocode}
+\DeclareRobustCommand{\VarX}[2][]{\ensuremath{\mathrm{Var}_{#1}\left[ {#2} \right]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\cVarX}
+% A conditional variance command is also provided, although less often
+% used.
+%    \begin{macrocode}
+\DeclareRobustCommand{\cVarX}[3][]{\ensuremath \mathrm{Var}_{#1}\left[ {#2} \big| {#3} \right]}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\eqlaw}
+% A shortcut for equality in law is provided.
+%    \begin{macrocode}
+\DeclareRobustCommand{\eqlaw}[0]{\mathop{\stackrel{(d)}{=}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tolaw}
+% |\tolaw| is a shortcut to a symbol for convergence in law.
+%    \begin{macrocode}
+\DeclareRobustCommand{\tolaw}[0]{\mathop{\stackrel{(d)}{\longrightarrow}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Stochastic processes}
+%
+% Some notation is customary when dealing with stochastic processes. Note 
+% that the same notation is sometimes used also in other parts of 
+% mathematics.
+%
+% \begin{macro}{\qvar}
+% The quadratic variation of two processes arises quite often. The command 
+% |\qvar|�gives the right bracket of two processes.
+%    \begin{macrocode}
+\DeclareRobustCommand{\qvar}[2]{\ensuremath{\left[ {#1},{#2} \right]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\cqvar}
+% Obviously, a shortcut for the conditional quadratic variation, or oblique
+% bracket is also provided.
+%    \begin{macrocode}
+\DeclareRobustCommand{\cqvar}[2]{\ensuremath{\langle {#1},\,{#2} \rangle}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Miscellany}
+% Some miscellaneous symbols or functions defined here.
+%
+% \begin{macro}{\1}
+% First, an indicator function, that prints a bold 1 and puts curly
+% braces.
+%    \begin{macrocode}
+\DeclareRobustCommand{\1}[1]{\ensuremath \mathbf{1}_{\{#1\}}}
+%    \end{macrocode}
+% \end{macro}
+% \Finale
-- 
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