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Efficient Simulation for Branching Linear Recursions
We consider a linear recursion of the form where is a
real-valued random vector with ,
is a sequence of i.i.d. copies of ,
independent of , and denotes
equality in distribution. For suitable vectors and
provided the initial distribution of is well-behaved, the process
is known to converge to the endogenous solution of the corresponding
stochastic fixed-point equation, which appears in the analysis of information
ranking algorithms, e.g., PageRank, and in the complexity analysis of divide
and conquer algorithms, e.g. Quicksort. Naive Monte Carlo simulation of
based on the branching recursion has exponential complexity in ,
and therefore the need for efficient methods. We propose in this paper an
iterative bootstrap algorithm that has linear complexity and can be used to
approximately sample . We show the consistency of estimators based on
our proposed algorithm.Comment: submitted to WSC 201
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