Stoc. Proc. Appl., (1998) ?, 105-133.
1991 Mathematics Subject Classification: 60J80
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, 1994a). 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 (iii) mild conditions for this family to be the only possible solutions.
There is an error in the statement of Proposition 3 and Corollary 3. In the first display in each case the logarithm of the right hand side is needed. The correct result was used in the arguments.
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