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Recursive estimation of distributional fix-points
- Part of
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- Journal:
- Journal of Applied Probability / Volume 37 / Issue 1 / March 2000
- Published online by Cambridge University Press:
- 14 July 2016, pp. 73-87
- Print publication:
- March 2000
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- Article
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In various stochastic models the random equation
of implicit renewal theory appears where the real random variable S and the stochastic process Ψ with index space and state space R are independent. By use of stochastic approximation the distribution function of S is recursively estimated on the basis of independent or ergodic copies of Ψ. Under integrability assumptions almost sure L1-convergence is proved. The choice of gains in the recursion is discussed. Applications are given to insurance mathematics (perpetuities) and queueing theory (stationary waiting and queueing times).
of implicit renewal theory appears where the real random variable 