Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \draw[line width=.6pt] (0.5,0.8) -- (4,0.8);
4 \node[font=\small,align=center] at (2.25,4.15) {$t=0$};
5 \path[draw=black,fill=black!12,line width=.6pt] (0.92,0.8) rectangle (1.83,3.4);
6 \node[font=\small,align=center,font=\scriptsize] at (1.375,0.5) {state 0};
7 \node[font=\small,align=center,font=\scriptsize] at (1.375,3.62) {$1$};
8 \path[draw=black,fill=black!12,line width=.6pt] (2.67,0.8) rectangle (3.58,0.8);
9 \node[font=\small,align=center,font=\scriptsize] at (3.125,0.5) {state 1};
10 \node[font=\small,align=center,font=\scriptsize] at (3.125,1.02) {$0$};
11 \draw[line width=.6pt] (5,0.8) -- (8.5,0.8);
12 \node[font=\small,align=center] at (6.75,4.15) {$t=\log(2)/2$};
13 \path[draw=black,fill=black!12,line width=.6pt] (5.42,0.8) rectangle (6.33,2.75);
14 \node[font=\small,align=center,font=\scriptsize] at (5.875,0.5) {state 0};
15 \node[font=\small,align=center,font=\scriptsize] at (5.875,2.97) {$\frac{3}{4}$};
16 \path[draw=black,fill=black!12,line width=.6pt] (7.17,0.8) rectangle (8.08,1.45);
17 \node[font=\small,align=center,font=\scriptsize] at (7.625,0.5) {state 1};
18 \node[font=\small,align=center,font=\scriptsize] at (7.625,1.67) {$\frac{1}{4}$};
19 \draw[line width=.6pt] (9.5,0.8) -- (13,0.8);
20 \node[font=\small,align=center] at (11.25,4.15) {$t=\log(2)$};
21 \path[draw=black,fill=black!12,line width=.6pt] (9.92,0.8) rectangle (10.83,2.425);
22 \node[font=\small,align=center,font=\scriptsize] at (10.375,0.5) {state 0};
23 \node[font=\small,align=center,font=\scriptsize] at (10.375,2.645) {$\frac{5}{8}$};
24 \path[draw=black,fill=black!12,line width=.6pt] (11.67,0.8) rectangle (12.58,1.775);
25 \node[font=\small,align=center,font=\scriptsize] at (12.125,0.5) {state 1};
26 \node[font=\small,align=center,font=\scriptsize] at (12.125,1.995) {$\frac{3}{8}$};
27 \node[font=\small,align=center,font=\scriptsize] at (7,4.6) {Each bar pair is an exact probability vector};
28 \end{tikzpicture}

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