Mixing
Transient or Recurrent behavior of Random walk on positive integer
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I know that the random walk on Z is transient or recurrent depending upon the probability. Now I think that the random walk on Z+ is also null recurrent or non-null recurrent or transient(probability of transition from i to i+1 is p and i+1 to i is q and from 0 to 0 is q, 0 to 1 is p where p+q=1, i>=0) depending on p. But I can't approach for the proper proof. please Help me. Thanks in advance.
markov-chains
asked 1 hour ago
Kousik Das
11
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up vote
0
down vote
favorite
I know that the random walk on Z is transient or recurrent depending upon the probability. Now I think that the random walk on Z+ is also null recurrent or non-null recurrent or transient(probability of transition from i to i+1 is p and i+1 to i is q and from 0 to 0 is q, 0 to 1 is p where p+q=1, i>=0) depending on p. But I can't approach for the proper proof. please Help me. Thanks in advance.
markov-chains
asked 1 hour ago
Kousik Das
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I know that the random walk on Z is transient or recurrent depending upon the probability. Now I think that the random walk on Z+ is also null recurrent or non-null recurrent or transient(probability of transition from i to i+1 is p and i+1 to i is q and from 0 to 0 is q, 0 to 1 is p where p+q=1, i>=0) depending on p. But I can't approach for the proper proof. please Help me. Thanks in advance.
markov-chains
asked 1 hour ago
Kousik Das
11
I know that the random walk on Z is transient or recurrent depending upon the probability. Now I think that the random walk on Z+ is also null recurrent or non-null recurrent or transient(probability of transition from i to i+1 is p and i+1 to i is q and from 0 to 0 is q, 0 to 1 is p where p+q=1, i>=0) depending on p. But I can't approach for the proper proof. please Help me. Thanks in advance.
markov-chains
markov-chains
asked 1 hour ago
Kousik Das
11
asked 1 hour ago
Kousik Das
11
asked 1 hour ago
Kousik Das
11
asked 1 hour ago
Kousik Das
11
asked 1 hour ago
Kousik Das
11
11
add a comment |
add a comment |
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