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• W2116748958 abstract "Let $A=(A_1,A_2,A_3,ldots)$ be a random sequence of non-negative numbers that are ultimately zero with $E[sum A_i]=1$ and $E left[sum A_{i} log A_i right] leq 0$. The uniqueness of the non-negative fixed points of the associated smoothing transform is considered. These fixed points are solutions to the functional equation $Phi(psi)= E left[ prod_{i} Phi(psi A_i) right], $ where $Phi$ is the Laplace transform of a non-negative random variable. The study complements, and extends, existing results on the case when $Eleft[sum A_{i} log A_i right]<0$. New results on the asymptotic behaviour of the solutions near zero in the boundary case, where $Eleft[sum A_{i} log A_i right]=0$, are obtained." @default.
• W2116748958 created "2016-06-24" @default.
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• W2116748958 date "2005-01-01" @default.
• W2116748958 modified "2023-10-17" @default.
• W2116748958 title "Fixed Points of the Smoothing Transform: the Boundary Case" @default.
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• W2116748958 doi "https://doi.org/10.1214/ejp.v10-255" @default.
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