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what is Space-Homogeneous?

A

abhishek wagle

Member
In chapter 3, section 5.3 simple random walk on S={...,-2,-2,0,1,2,3,...} it has been stated that simple random walk is space homogeneous. what exactly does space homogeneous mean? and how does it apply to srw? i am not able to undertand the core reading.
 
Space-homogeneous is described in the ActEd text directly underneath this Core Reading.

Time-homogeneous means that the probabilities do not depend on the actual times themselves, just the time interval.
Space-homogeneous means that the probabilities do not depend on the actual states involved, just the distance between them.
 
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