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+% arara: indent: {overwrite: true, silent: on}
+\documentclass[png,border=10pt,tikz]{standalone}
+\usepackage{xstring}
+\usepackage{tikz}
+\usetikzlibrary{calc}
+
+\pgfkeys{/tikz/.cd,
+ vertical factor/.initial=0.5,
+ vertical factor/.get=\vertfactor,
+ vertical factor/.store in=\vertfactor,
+ start coordinate/.initial={0,\vertfactor},
+ start coordinate/.get=\startcoord,
+ start coordinate/.store in=\startcoord,
+ sample color/.initial=black,
+ sample color/.get=\samplecol,
+ sample color/.store in=\samplecol,
+ sample size/.initial=1pt,
+ sample size/.get=\samplesize,
+ sample size/.store in=\samplesize,
+ sample line width/.initial=very thick,
+ sample line width/.get=\samplelinewidth,
+ sample line width/.store in=\samplelinewidth,
+}
+
+
+\newcommand{\samplepath}[1]{%
+ \coordinate (start) at (\startcoord) ;
+ \foreach \samples[count=\xi from 1] in {#1}{%
+ \StrCut{\samples}{|}{\vertdir}{\hordir}
+ \ifnum\xi=1
+ \draw[\samplelinewidth,\samplecol](start)
+ --++(\hordir,0) coordinate (start);
+ \else
+ \IfStrEq{\vertdir}{+}{%true
+ \draw[\samplelinewidth,\samplecol]($(start)+(0,\vertfactor)$)
+ --++(\hordir,0)coordinate(start);
+ }{%false
+ \relax
+ }
+ \IfStrEq{\vertdir}{-}{%true
+ \draw[\samplelinewidth,\samplecol]($(start)+(0,-\vertfactor)$)
+ --++(\hordir,0)coordinate(start);
+ }{%false
+ \relax
+ }
+ \fi
+ }
+}
+
+\tikzset{sample/.style={
+ circle,
+ inner sep=\samplesize,
+ fill=\samplecol,
+ }
+}
+
+\newcommand{\discretesamplepath}[1]{%
+ \coordinate (start) at (\startcoord) ;
+ \foreach \samples[count=\xi from 1] in {#1}{%
+ \StrCut{\samples}{|}{\vertdir}{\hordir}
+ \ifnum\xi=1
+ \path(start)node[sample]{}
+ --++(\hordir,0) coordinate (start);
+ \else
+ \IfStrEq{\vertdir}{+}{%true
+ \path($(start)+(0,\vertfactor)$)node[sample]{}
+ --++(\hordir,0)coordinate(start);
+ }{%false
+ \relax
+ }
+ \IfStrEq{\vertdir}{-}{%true
+ \path($(start)+(0,-\vertfactor)$)node[sample]{}
+ --++(\hordir,0)coordinate(start);
+ }{%false
+ \relax
+ }
+ \fi
+ }
+}
+
+\begin{document}
+\begin{tikzpicture}
+ % axis
+ \draw[-stealth] (0,-1)--(0,4) node[left]{$X(t)$};
+ \draw[-stealth] (-1,0)--(5,0) node[below]{$t$};
+ \samplepath{+|0.5,+|0.25,-|1.5,+|1,+|0.5,+|0.75}
+\end{tikzpicture}
+\end{document}