% Compilation options
\synctex=1

% Packages
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenx}
\usepackage[english]{babel}
\usepackage{microtype}
\usepackage{fancyhdr}
\usepackage{listings}
\usepackage{appendix}
\usepackage{vmargin}
\usepackage{setspace}
\usepackage{mathrsfs}
\usepackage{mathenv}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amscd}
\usepackage{amsthm}
\usepackage{mathrsfs}
\usepackage{graphicx}
\usepackage{epstopdf}
\usepackage{subfigure}
\usepackage{color}
\usepackage{todonotes}
\usepackage{caption}
\usepackage[numbers]{natbib}
\usepackage{hyperref}
\usepackage{cleveref}

% Packages options
\hypersetup{citecolor=blue, colorlinks=true, linkcolor=[rgb]{0.,0.,0.7}}
\graphicspath{{figures/}}

% Macros
\definecolor{darkred}{rgb}{.7,0,0}
\newcommand{\real}[0]{\mathbf{R}}
\newcommand{\nat}[0]{\mathbf{N}}
\newcommand{\op}[0]{\mathcal}
\newcommand{\grad}[0]{\nabla}
\newcommand{\dive}[0] {\,\nabla\,\cdot\,}
\newcommand{\ip}[2]{\left\langle{#1,#2}\right\rangle}
\newcommand{\norm}[1]{\left\| #1 \right\|}
\newcommand{\pard}[2]{\partial_{#2} #1}
\newcommand{\pardl}[2]{\frac{\partial{#1}}{\partial{#2}}}
\newcommand{\pardd}[2]{\partial_{#2}^2 #1}
\newcommand{\parddl}[2]{\frac{\partial^2{#1}}{\partial{#2}^2}}
\newcommand{\hermite}[0]{\mathcal}
\newcommand{\gaussian}[1]{g_{#1}}
\newcommand{\stdgaussian}[0]{g}
\newcommand{\test}[1]{C^\infty_c (#1)}
\newcommand{\flp}[2]{L^{#1} (#2)}
\newcommand{\wlp}[3]{L^{#1} (#2,#3)}
\newcommand{\sobolev}[2]{H^{#1} (#2)}
\newcommand{\wsobolev}[3]{H^{#1} (#2, #3)}
\newcommand{\red}[1]{\textcolor{darkred}{#1}}
\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
\newcommand{\smooth}[1]{C^\infty(#1)}
\newcommand{\cont}[2]{C^{#1} (#2)}
\newcommand{\contb}[2]{C_b^{#1} (#2)}
\newcommand{\Space}[0]{\mathscr}
\newcommand{\expect}[0]{\mathbb{E}}
\newcommand{\dotx}[0]{\,\cdot\,}
\newcommand{\abs}[1]{\left| #1 \right|}

% Redefinitions
\renewcommand{\d}[0]{\,\mathrm{d}}

% Layout options
\setlength{\parskip}{6pt}
\setstretch{1.3}

% Setting for the table of contents
\setcounter{secnumdepth}{1}
\setcounter{tocdepth}{1}

% Theorems
\theoremstyle{plain}
\newtheorem{assumption}{Assumption}[section]
\newtheorem{example}{Example}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{axiom}[theorem]{Axiom}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}