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- W2009587040 abstract "We study the asymptotic behaviour of the solution of the stochastic difference equation $X_{n+1} = X_n + g(X_n)(1 + xi_{n+1})$, where $g$ is a positive function, $(xi_n)$ is a 0-mean, square-integrable martingale difference sequence, and the states $X_n < 0$ are assumed to be absorbing. We clarify, under which conditions $X_n$ diverges with positive probability, satisfies a law of large numbers, and, properly normalized, converges in distribution. Controlled Galton-Watson processes furnish examples for the processes under consideration." @default.
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- W2009587040 date "1987-01-01" @default.
- W2009587040 modified "2023-09-26" @default.
- W2009587040 title "On the Asymptotic Behaviour of Discrete Time Stochastic Growth Processes" @default.
- W2009587040 doi "https://doi.org/10.1214/aop/1176992272" @default.
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