Blackwell's renewal theorem for certain linear submartingales and coupling

Gerold Alsmeyer

doi:10.1007/bf00994262

On coupling of random walks and renewal processes

Journal of Applied Probability ◽

10.2307/3215269 ◽

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 complete coupling proof of Blackwell's renewal theorem

Stochastic Processes and their Applications ◽

10.1016/0304-4149(87)90052-4 ◽

1987 ◽

Vol 26 ◽

pp. 87-97 ◽

Cited By ~ 12

Author(s):

Hermann Thorisson

Keyword(s):

Renewal Theorem ◽

Blackwell's Renewal Theorem

Generalizations of the arithmetic case of Blackwell’s renewal theorem

Statistics & Probability Letters ◽

10.1016/j.spl.2019.01.031 ◽

2019 ◽

Vol 149 ◽

pp. 124-131

Author(s):

Petros Hadjicostas

Keyword(s):

Renewal Theorem ◽

Blackwell's Renewal Theorem

A Probabilistic Proof of Blackwell's Renewal Theorem

The Annals of Probability ◽

10.1214/aop/1176995810 ◽

1977 ◽

Vol 5 (3) ◽

pp. 482-485 ◽

Cited By ~ 30

Author(s):

Torgny Lindvall

Keyword(s):

Renewal Theorem ◽

Probabilistic Proof ◽

Blackwell's Renewal Theorem

Simplified analytical proof of Blackwell's renewal theorem

Statistics & Probability Letters ◽

10.1016/j.spl.2005.04.022 ◽

2005 ◽

Vol 74 (1) ◽

pp. 15-20 ◽

Cited By ~ 1

Author(s):

Jürgen Dippon ◽

Harro Walk

Keyword(s):

Renewal Theorem ◽

Analytical Proof ◽

Blackwell's Renewal Theorem

A probabilistic proof of Blackwell's renewal theorem

Advances in Applied Probability ◽

10.2307/1426381 ◽

1977 ◽

Vol 9 (2) ◽

pp. 236-236 ◽

Cited By ~ 1

Author(s):

Torgny Lindvall

Keyword(s):

Renewal Theorem ◽

Probabilistic Proof ◽

Blackwell's Renewal Theorem

A Note on Blackwell's Renewal Theorem

Journal of Mathematical Sciences ◽

10.1023/b:joth.0000027035.44184.7e ◽

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 local limit theorems and Blackwell's renewal theorem for independent random variables

Annals of the Institute of Statistical Mathematics ◽

10.1007/bf02504668 ◽

1975 ◽

Vol 27 (1) ◽

pp. 507-520 ◽

Cited By ~ 4

Author(s):

Makoto Maejima

Keyword(s):

Limit Theorems ◽

Random Variables ◽

Local Limit ◽

Independent Random Variables ◽

Renewal Theorem ◽

Local Limit Theorems ◽

Blackwell's Renewal Theorem

A probabilistic proof of Blackwell's renewal theorem

Advances in Applied Probability ◽

10.1017/s0001867800043949 ◽

1977 ◽

Vol 9 (02) ◽

pp. 236

Author(s):

Torgny Lindvall

Keyword(s):

Renewal Theorem ◽

Probabilistic Proof ◽

Blackwell's Renewal Theorem

On coupling of random walks and renewal processes

Journal of Applied Probability ◽

10.1017/s0021900200103778 ◽

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.