Martingale Convergence and Large Deviations in the Branching Random Walk

1993 ◽  
Vol 37 (2) ◽  
pp. 269-273
Author(s):  
J. D. Biggins
Keyword(s):  
Random Walk ◽  
Large Deviations ◽  
Branching Random Walk ◽  
Martingale Convergence

Martingale convergence in the branching random walk

1977 ◽  
Vol 14 (01) ◽  
pp. 25-37 ◽  
Author(s):  
J. D. Biggins
Keyword(s):  
Random Walk ◽  
Branching Random Walk ◽  
Malthusian Parameter ◽  
Martingale Convergence ◽  
Special Case

A result like the Kesten-Stigum theorem is obtained for certain martingales associated with the branching random walk. A special case, when a ‘Malthusian parameter’ exists, is considered in greater detail and a link with some known results about the Crump-Mode model for a population is established.

Martingale convergence in the branching random walk

1977 ◽  
Vol 14 (1) ◽  
pp. 25-37 ◽  
Author(s):  
J. D. Biggins
Keyword(s):  
Random Walk ◽  
Branching Random Walk ◽  
Malthusian Parameter ◽  
Martingale Convergence ◽  
Special Case

A result like the Kesten-Stigum theorem is obtained for certain martingales associated with the branching random walk. A special case, when a ‘Malthusian parameter’ exists, is considered in greater detail and a link with some known results about the Crump-Mode model for a population is established.

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