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I am trying to understand why Random Walks' and Random Jumps', on a graph, transition matrix are also stochastic matrix.

A stochastic matrix is a matrix the values of each row add up to 1 and no value is < 0.

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    What about if you include a Random Walk that can also have jumps? Where these jumps have a certain probability also. What I mean by this is lets say your at A now you have some probability to go from A to B, because of random walk, BUT now you also have another probability to jump from A to C! How would that be a stochastic matrix compared to the original of random walking alone.2011-12-12

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