Lindley-type equations in the branching random walk

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Abstract

An analogue of the Lindley equation for random walk is studied in the context of the branching random walk, taking up the studies of Karpelevich, Kelbert and Suhov [(1993a) In: Boccara, N., Goles, E., Martinez, S., Picco, P. (Eds.), Cellular Automata and Cooperative Behaviour. Kluwer, Dordrecht, pp. 323–342; (1994a) Stochast. Process. Appl. 53, 65–96]. The main results are: (i) close to necessary conditions for the equation to have a solution, (ii) mild conditions for there to be a one-parameter family of solutions and (iii) mild conditions for this family to be the only possible solutions.

MSC

primary 60J80

Keywords

Maxima
Extreme values
Functional equations

Cited by (0)

1

This work was started whilst visiting the Institute of Mathematics and its Applications, University of Minnesota during the programme on `Emerging Applications of Probability Theory’. I am happy to thank the IMA for its excellent support, and the NSF, NSA and ARO for their financial assistance via the IMA.