【 在 mypeony 的大作中提到: 】
: 这玩意晚上有转换器的
: 类似公式编辑器编辑完,一键转码就行
: 有啥好折腾的
不懂装懂的人说出来全是你这种外行话,来来来,说说我这段代码咋一键转码:
\begin{frame}{两个状态的Markov链(一般情形)}
\begin{columns}
\column{0.5\textwidth}
\centering
初始概率分布\(\mathbf{p}^{(0)} = (p_0, q_0)\).\\[.2cm]
转移矩阵\(T =
\begin{pmatrix}
1 - \alpha & \alpha \\
\beta & 1 - \beta
\end{pmatrix}\).
\column{0.5\textwidth}
\begin{tikzpicture}[scale = 1, tikzdot3, shorten >=1pt, node distance=2cm, auto]
\node[state,fill=bg3] (P) {P};
\node[state,fill=bg3] (Q) [right of=P] {Q};
\path[->]
(P) edge [loop left] node {\(1 - \alpha\)} ()
edge [bend left] node {\(\alpha\)} (Q)
(Q) edge [loop right] node {\(1 - \beta\)} ()
edge [bend left] node {\(\beta\)} (P);
\end{tikzpicture}
\end{columns}\pause{}
\vspace{.2cm}
\(p_n = (1-\alpha)p_{n-1} + \beta q_{n-1}\),
\(q_n = \alpha p_{n-1} + (1-\beta)q_{n-1}\).\\\pause{}
写成矩阵乘法
\(\mathbf{p}^{(n)} = (p_n, q_n) = (p_{n-1}, q_{n-1}) T =
\mathbf{p}^{(n-1)} T\).\\\pause{}
故第\(n\)步后概率分布\(\mathbf{p}^{(n)} = \mathbf{p}^{(0)} T^n\).\pause{}
记\(\lambda = 1-\alpha-\beta\),\(|\lambda|<1\).\\
\(p_n = (1-\alpha)p_{n-1} + \beta (1-p_{n-1})
=(1-\alpha-\beta)p_{n-1} + \beta = \lambda p_{n-1} + \beta\).\\\pause{}
% \(q/(p-1) = - \beta/(\alpha + \beta)\).
\(p_n = (p_0 - \beta/(\alpha + \beta))\lambda^n + \beta/(\alpha + \beta)\).
\(\lim_{n \to \infty} p_n = \beta/(\alpha + \beta)\).\\\pause{}
\(q_n = (q_0 - \alpha/(\alpha + \beta))\lambda^n + \alpha/(\alpha + \beta)\).
\(\lim_{n \to \infty} q_n = \alpha/(\alpha + \beta)\).\\\pause{}
极限分布\(\mathbf{p}^{(\infty)}
= \lim_{n \to \infty} \mathbf{p}^{(n)} = (\beta/(\alpha + \beta), \alpha/(\alpha + \beta))\).
\end{frame}
--
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