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] (0.4,0.65) -- (6.1,0.65);
4 \node[font=\small,align=center] at (3.25,3.85) {Observable $f$};
5 \path[draw=black,fill=black!12,line width=.6pt] (0.742,0.65) rectangle (1.483,0.65);
6 \node[font=\small,align=center,font=\scriptsize] at (1.1125,0.35) {0};
7 \node[font=\small,align=center,font=\scriptsize] at (1.1125,0.87) {$0$};
8 \path[draw=black,fill=black!12,line width=.6pt] (2.167,0.65) rectangle (2.908,2.12);
9 \node[font=\small,align=center,font=\scriptsize] at (2.5375,0.35) {1};
10 \node[font=\small,align=center,font=\scriptsize] at (2.5375,2.34) {$3$};
11 \path[draw=black,fill=black!12,line width=.6pt] (3.592,0.65) rectangle (4.333,1.63);
12 \node[font=\small,align=center,font=\scriptsize] at (3.9625,0.35) {2};
13 \node[font=\small,align=center,font=\scriptsize] at (3.9625,1.85) {$2$};
14 \path[draw=black,fill=black!12,line width=.6pt] (5.017,0.65) rectangle (5.758,3.1);
15 \node[font=\small,align=center,font=\scriptsize] at (5.3875,0.35) {3};
16 \node[font=\small,align=center,font=\scriptsize] at (5.3875,3.32) {$5$};
17 \draw[line width=.6pt] (7.6,0.65) -- (13.3,0.65);
18 \node[font=\small,align=center] at (10.45,3.85) {Conditional expectation $Ef$};
19 \path[draw=black,fill=black!12,line width=.6pt] (7.942,0.65) rectangle (8.683,1.63);
20 \node[font=\small,align=center,font=\scriptsize] at (8.3125,0.35) {0};
21 \node[font=\small,align=center,font=\scriptsize] at (8.3125,1.85) {$2$};
22 \path[draw=black,fill=black!12,line width=.6pt] (9.367,0.65) rectangle (10.108,1.63);
23 \node[font=\small,align=center,font=\scriptsize] at (9.7375,0.35) {1};
24 \node[font=\small,align=center,font=\scriptsize] at (9.7375,1.85) {$2$};
25 \path[draw=black,fill=black!12,line width=.6pt] (10.792,0.65) rectangle (11.533,2.47);
26 \node[font=\small,align=center,font=\scriptsize] at (11.1625,0.35) {2};
27 \node[font=\small,align=center,font=\scriptsize] at (11.1625,2.69) {$\frac{26}{7}$};
28 \path[draw=black,fill=black!12,line width=.6pt] (12.217,0.65) rectangle (12.958,2.47);
29 \node[font=\small,align=center,font=\scriptsize] at (12.5875,0.35) {3};
30 \node[font=\small,align=center,font=\scriptsize] at (12.5875,2.69) {$\frac{26}{7}$};
31 \node[font=\small,align=center,font=\scriptsize] at (7,4.45) {Weights $\pi=(1,2,3,4)/10$; the block values are 2 and $26/7$.};
32 \end{tikzpicture}

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