Hidden Markov model: Difference between revisions

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m Fixed the link for Borel set.
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* <math>\operatorname{\mathbf{P}}\bigl(Y_n \in A\ \bigl|\ X_1=x_1,\ldots,X_n=x_n\bigr)=\operatorname{\mathbf{P}}\bigl(Y_n \in A\ \bigl|\ X_n=x_n\bigr),</math>
 
:for every <math>n\geq 1,</math> <math>x_1,\ldots, x_n,</math> and every [[Borel set|Borel]] set <math>A</math>.
 
Let <math>X_t</math> and <math>Y_t</math> be continuous-time stochastic processes. The pair <math>(X_t,Y_t)</math> is a ''hidden Markov model'' if