Simplified analytical proof of Blackwell's renewal theorem

2005 ◽  
Vol 74 (1) ◽  
pp. 15-20 ◽  
Author(s):  
Jürgen Dippon ◽  
Harro Walk
Keyword(s):  
Renewal Theorem ◽  
Analytical Proof ◽  
Blackwell's Renewal Theorem

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

A Note on Blackwell's Renewal Theorem

2004 ◽  
Vol 121 (5) ◽  
pp. 2688-2691
Author(s):  
E. A. M. Omey ◽  
J. L. Teugels
Keyword(s):  
Renewal Theorem ◽  
Blackwell's Renewal Theorem

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (01) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

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