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%% Journal selection: ECP or EJP.                                %%
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\documentclass[ECP]{ejpecp} % replace ECP by EJP if needed.  

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%\usepackage[T1]{fontenc}
%\usepackage[utf8]{inputenc}

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%\usepackage{enumerate}  % uncomment to use this package

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\AUTHORS{%
  Krzysztof~Burdzy\footnote{University of Washington, USA. E-mail:
    burdzy@math.washington.edu}
  \and % remove this line and below if single author
  Djalil~Chafa\"{\i}\footnote{Universit\'e Paris-Est Marne-la-Vall\'ee,
    France. E-mail: djalil@chafai.net} }%AUTHORS

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\TITLE{Introduction to the \emph{ejpecp} Class Version 0.5\THANKS{Supported by
    the Institute of Mathematical Statistics (IMS) and the Bernoulli
    Society.}} %\THANKS is optional

\SHORTTITLE{Introduction to the \emph{ejpecp} Class}

\KEYWORDS{EJP ; ECP ; typesetting ; LaTeX} % Separate items with ;

\AMSSUBJ{NA} % Separate items with ;
%\AMSSUBJSECONDARY{FIXME:} % Optional, separate items with ;

\SUBMITTED{January 1, 2012} % Edit.
\ACCEPTED{January 1, 2012} % Edit.

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%\ARXIVID{NNNN.NNNN}

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\VOLUME{0}
\YEAR{2012}
\PAPERNUM{0}
\PAGESTART{0}
\PAGEEND{0}
%\DOI{}

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\ABSTRACT{The $\LaTeXe$ class \emph{ejpecp} is designed for typesetting of
  articles to be published in the research periodicals \emph{Electronic
    Journal of Probability} (EJP) and \emph{Electronic Communications in
    Probability} (ECP).}

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%% Please add your own macros and environments below:            %%
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%% Avoid using \def if possible and use instead \newcommand      %%
%% The usage of \def is a bad habit producing unexpected errors  %%
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%% Avoid defining your own environments, and use instead         %%
%% the available environments already defined by ejpecp:         %%
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%% definition, theorem, remark, lemma, corollary, example, proof %%
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\newcommand{\ABS}[1]{\left(#1\right)} % example of author macro
\newcommand{\veps}{\varepsilon} % another example of author macro

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\begin{document}

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The $\LaTeXe$ class ejpecp is designed for typesetting of articles for the
Electronic Journal of Probability (EJP) and Electronic Communications in
Probability (ECP). The ejpecp class comes with a commented sample file called
\texttt{sample.tex}. You are probably reading the pdf version of this sample
file, compiled with a pdflatex engine.

\textbf{An easy way to prepare an article for publication in EJP/ECP is to
  edit the source file \texttt{sample.tex} for this document. Replace the main
  body of the file with the main body of your article. Supply all metadata
  (title, authors, abstract, etc) that are requested in the latex file.}

The ejpecp class works only with the pdflatex engine, generating pdf files.
You need a copy of the \texttt{ejpecp.cls} file in your directory\footnote{Or
  in any directory scanned for \texttt{cls} files by your pdflatex engine.}in
order to compile documents based on the ejpecp class, such as
\texttt{sample.tex}. To configure the ejpecp class for ECP, use
\begin{verbatim}
\documentclass[ECP]{ejpecp}
\end{verbatim}
while for EJP, use
\begin{verbatim}
\documentclass[EJP]{ejpecp}
\end{verbatim}
The ejpecp document class loads automatically the following standard packages
\footnote{For your information, the following packages are also loaded: bera,
  geometry, hyperref, xstring.}:
\begin{center}
  amsmath, amsthm, amsfonts, amssymb, latexsym, dsfont, graphicx
\end{center}
It is therefore not necessary to add \verb+\usepackage+ load commands for
these packages to your latex file. However, you may want to load additional
packages, such as the enumerate package, by using \verb+\usepackage+ commands.
The precise location of these extra load commands is clearly mentioned in the
\texttt{sample.tex} file. The ejpecp class provides various environments, and
also important commands such as \verb+\AUTHORS+, \verb+\TITLE+, etc.
 
\section{Standard predefined environments}

One of the main features of the ejpecp class is its predefined environments.

 \begin{theorem}[My theorem]\label{th:1}
   This is the body of the theorem. This theorem has a name between
   parentheses, and this is implemented by adding an optional parameter
   between square brackets to the theorem environment, namely
\begin{verbatim}
   \begin{theorem}[My theorem] \label{th:1}
     This is the body of ...
   \end{theorem}
\end{verbatim}
 \end{theorem}

 \begin{proof}[Proof of Theorem \ref{th:1}]
   This is the body of the proof of the theorem above. This proof has a name,
   and this is implemented by adding an optional parameter between square
   brackets to the proof environment, namely
   \begin{verbatim}
   \begin{proof}[Proof of Theorem \ref{th:1}] 
     This is the body of the proof of ... 
   \end{proof} 
   \end{verbatim}
   We recommend that you give names to most of your theorem-like environments.
   You cannot imagine how this helps your readers! The proof ends at the
   square box.
 \end{proof}

 Note that a square box $\square$ is automatically added at the end of the
 proof by the environment ``proof.'' The ejpecp class provides several default
 environments: theorem, proof, lemma, proposition, definition, corollary,
 remark, example, problem, conjecture.

 \begin{lemma}[My lemma]
   Body of the Lemma. 
 \end{lemma}

 \begin{proof}
   This is the body of a proof environment without name, obtained using
\begin{verbatim}
\begin{proof} 
  This is the body of ... 
\end{proof}
\end{verbatim}
   Note again the automatic inclusion of a square box at the right place $\to$
 \end{proof}

Here are some more examples of predefined environments:

 \begin{lemma}
   Body of the Lemma. This lemma does not have a name.
 \end{lemma}

 \begin{proposition}[My proposition]
   Body of the proposition.
 \end{proposition}

 \begin{corollary}[My corollary]
   Body of the corollary.
 \end{corollary}

 \begin{definition}[My definition]
   Body of the definition.
 \end{definition}

 \begin{conjecture}[My conjecture]
   Body of the conjecture.
 \end{conjecture}

 \begin{remark}[My remark]
   Body of the remark. Note that the style of the body differs from the one
   used for theorems.
 \end{remark}

 \begin{example}[My example]
   Body of the example.
 \end{example}

 \begin{problem}[My problem]
   Body of the problem.
 \end{problem}

 These environments cover most author's needs. It is possible -- but not
 recommended at all! -- to define additional environments based on the theorem
 environment.

\section{Section headings}

The default size for section titles in \LaTeX\ is a bit large. As you might have
noticed, the ejpecp class provides smaller section titles. Here are some
sub-sections:

\subsection{A sub-section}

\subsubsection{A sub-sub-section}

\section{How to include graphics}

You may include graphics in PDF or EPS or JPEG or PNG format as follows

\begin{verbatim}
\begin{figure}[htbp]
  \begin{center}
    \includegraphics[scale=1.0]{filename}
    \caption{This is my figure.}
    \label{fi:myfigure}
  \end{center}
\end{figure}
\end{verbatim}

Note that in a figure environment, the \verb+\label+ should always appear
after a \verb+\caption+ in order to produce a valid reference to the figure.
You may play with the options \verb+[htbp]+ (see the \LaTeXe\ documentation
for their meaning) and with the options of the \verb+\includegraphics+ command
(see the documentation of the graphicx package).

\section{How to write a good LaTeX code}

All mathematicians believe that the mathematical results are the most
important elements of an article. Many of them believe that the aesthetic
aspects of the proof are also important. Some of them believe that even the
writing style is important. Few of them believe that the \LaTeX\ code needs to
be elegant.

A good \LaTeX\ code is easier to maintain, to convert, and to read. It helps
your co-authors, and helps to speed up the publication process. Here are some
suggestions:

\begin{itemize}\addtolength{\itemsep}{-0.5\baselineskip}
\item never use \verb+\def+ for defining macros, use instead
  \verb+\newcommand+
\item never use \verb+$$+ for displayed equations, use instead the brackets
  \verb+\[ \]+
\item use \verb+\textbf{}+, \verb+\textit{}+, and \verb+\emph{}+ instead of
  \verb+{\bf }+, \verb+{\it }+, and \verb+{\em }+
\item never use one letter names for macros or for environments
\item never use strange names for macros and environments
\item use the environment proof provided by amsmath (as in ejpecp)
\item use \verb+\newenvironment+ to define new environments
\item use \verb+\binom{n}{k}+ instead of \verb+n \choose k+
\item use \verb+\frac{a}{b}+ instead of a \verb+\over b+
\item never use an exotic package if you do not really need it
\item indent your code and avoid too long lines
\item use prefixed labels such as \verb+eq:+ for equations and \verb+th:+ for
  theorems
\item to produce graphics, avoid using \emph{psfrag} or \emph{XFig} and use
  instead \emph{\href{http://en.wikipedia.org/wiki/Ipe_(program)}{Ipe}}
\item learn how to interpret the error messages generated during compilation
\item read the wiki-books on \href{http://en.wikibooks.org/wiki/LaTeX}{LaTeX}
  and \href{http://en.wikibooks.org/wiki/LaTeX/Mathematics}{LaTeX Maths}
\end{itemize}

Some authors prefer \TeX\ instead of \LaTeX. We believe that \TeX\ is a good
program. However EJP and ECP need a standardized layout for all papers, and
this is easier done with \LaTeX\ than with \TeX. For that reason, you should
use \LaTeX. The latest major version of \LaTeX\ is called \LaTeXe. It is
important to learn how to write genuine \LaTeXe\ code (see above), rather than
a mixture of \TeX\ and old \LaTeX\ (prior to \LaTeXe).
 
\section{Version number}

The version number of the ejpecp class converges to
the Euler-Mascheroni constant 
\[
\gamma 
= \lim_{n\to\infty}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}-\ln(n)\right)
= 0.57721\cdots
\]
which is sequence \href{http://oeis.org/A001620}{A001620} in the
\href{http://oeis.org}{On-Line Encyclopedia of Integer Sequences} of Sloane.
As you probably know, it turns out that the Euler-Mascheroni constant $\gamma$
is the mean of the Gumbel distribution which has cumulative distribution
function $t\in\mathbb{R}\mapsto e^{-e^{-t}}$.

\section{How to help us}

We (KB and DC) do not consider ourselves \LaTeXe\ experts.
We will be happy to receive comments and suggestions for improvement
(especially constructive ones).

\section{How to include bibliography}

The bibliography should be included in your document (not a separate file),
inside the standard environment \verb+\thebibliography+. If you use bibtex,
this can be accomplished by including the \texttt{bbl} file inside your
document (after preliminary compilation with latex and bibtex). The
bibliography should be sorted alphabetically according to authors names, and
the records should be labeled by numbers. Math Reviews numbers should be
included as in the sample below. If you use bibtex, use
\verb+\bibliographystyle{amsplain}+. Here is an example of bibliography:

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%% Use the two commands below for producing your bibliography    %%
%% with bibtex, then comment again the commands and include the  %%
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%\bibliographystyle{amsplain}
%\bibliography{yourbibfilename}

% add below the content of your .bbl file produced by bibtex.

\begin{thebibliography}{99}

\bibitem{doob} Doob, J. L.: Heuristic approach to the Kolmogorov-Smirnov
  theorems. \emph{Ann. Math. Statistics} \textbf{20}, (1949), 393--403.
  \MR{0030732}

\bibitem{gnekol} Gnedenko, B. V. and Kolmogorov, A. N.: Limit distributions for
  sums of independent random variables. Translated and annotated by K. L.
  Chung. With an Appendix by J. L. Doob. \emph{Addison-Wesley}, Cambridge,
  1954. ix+264 pp. \MR{0062975}

\bibitem{ito} It\^o, K.: Multiple Wiener integral. \emph{J. Math. Soc. Japan}
  \textbf{3}, (1951), 157--169. \MR{0044064}

\bibitem{levy} L\'evy, P.: Sur certains processus stochastiques homog\`enes.
  \emph{Compositio Math.} \textbf{7}, (1939), 283--339. \MR{0000919}

\end{thebibliography}
 
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\end{document}

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