绘制布朗运动,用虚线表示值

绘制布朗运动,用虚线表示值

我想在 LaTeX 中制作一个类似于下图的图(通过 TikZ 或其他工具)。我已经找到了一种绘制布朗路径的方法。但是,我不知道如何添加下图所示的虚线。这些线是在布朗路径达到特定值时生成的,标签将是字母而不是数字。谢谢!

一个例子

实际上,我找到的绘制布朗路径的方法在这里: 如何在 tikz/pgf 中绘制布朗运动

我不需要像该链接中的答案那样添加上限或下限。但是,我确实需要为某些特定值添加一些虚线。

答案1

以下是使用元帖子包裹在luamplib。使用 进行编译lualatex,请点击链接获取更多详细信息。

在此处输入图片描述

\RequirePackage{luatex85}
\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);

% set a seed, so it is repeatable (it will work fine if you 
% delete this, but you will get a different path...)
randomseed := 1288.27463;

numeric a, u, v, wt, N, hi, lo;
% parameters
a = 0;
N = 100;
lo = -hi = infinity;
wt = 2/5; % weight - larger = more random

% scales
u = 1mm; % scale
v = 1cm;

% make the brownian path, keeping track of the hi and lo points
% you could use uniformdeviate or calculate a more complicated
% distribution here instead of "normaldeviate"
path A;
A = (origin for t=1 upto N: 
        hide( 
            if a>hi: hi := a; fi if a<lo: lo := a; fi 
            a := a + wt * normaldeviate; 
        )
        -- (t,a) 
     endfor) xscaled u yscaled v;

% draw in the axes nicely
drawoptions(withcolor 1/2 white);
draw ((0,lo)--(0,hi)) scaled v;
for i=ceiling(lo) upto floor(hi) : 
    draw (left--right) scaled 2 shifted (0,i*v);
    label.lft("$" & decimal i & "$", (0,i*v)); 
endfor
draw (origin--right) scaled (N*u);

% draw the markers at the desired points along the brownian motion path
drawoptions(dashed evenly scaled 1/2 withcolor 2/3 blue);

z0 = point 44 of A; 
draw (x0,-16) -- z0 -- (-16,y0); 
label.bot("$T_0$", (x0,-16));
label.lft("$M_0$", (-16,y0));

z1 = point 81 of A; 
draw (x1,-16) -- z1 -- (-16,y1); 
label.bot("$T_1$", (x1,-16));
label.lft("$M_1$", (-16,y1));

% etc...

% finally draw the path on top of everything else
drawoptions(withcolor 2/3 red);
draw A;

drawoptions();
endfig;
\end{mplibcode}
\end{document}

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