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1. • CommentRowNumber1.
   • CommentAuthorIan_Durham
   • CommentTimeMar 22nd 2010
   • PermaLink
   Author: Ian_Durham
   Format: HtmlI posted a quick query on [[Markov chain]]s.

   I posted a quick query on Markov chains.
2. • CommentRowNumber2.
   • CommentAuthorEric
   • CommentTimeMar 22nd 2010
   • (edited Mar 22nd 2010)
   • PermaLink
   Author: Eric
   Format: MarkdownYep yep. My experience is only with finite state spaces, where the Markov process is described by a transition matrix (see <a href="http://en.wikipedia.org/wiki/Markov_chain">Wikipedia</a>). In that case, you have a directed edge from state <latex>x</latex> to state <latex>y</latex> labeled by a transition probability <latex>p_{x,y}</latex>. Note: I should be more careful. Sometimes, I like to "explode" categories into [[category of elements]]. For example, if we are thinking about sets <latex>X</latex>,<latex>Y</latex> and a function <latex>f:X\to Y</latex> sometimes I like to "explode" this so we have one morphism <latex>f_{x,y}</latex> for each <latex>x\in X</latex> and <latex>y = f(x)</latex>.

   Yep yep. My experience is only with finite state spaces, where the Markov process is described by a transition matrix (see Wikipedia). In that case, you have a directed edge from state to state labeled by a transition probability .

   Note: I should be more careful. Sometimes, I like to "explode" categories into category of elements. For example, if we are thinking about sets , and a function sometimes I like to "explode" this so we have one morphism for each and .