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# Mariana Olvera-Cravioto, University of California, Berkeley

## January 10, 2018 @ 2:30 pm - 3:30 pm

**Efficient simulation for branching recursions**

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A variety of problems in science and engineering, ranging from population and statistical physics models to the study of queueing systems, computer networks and the internet, lead to the analysis of branching distributional equations. The solutions to these equations are not in general analytically tractable, and hence need to be computed numerically. This talk discusses a simulation algorithm known as “Population Dynamics”, which is designed to produce a pool of identically distributed observations having approximately the same law as the attracting endogenous solution in a wide class of branching distributional equations.

The Population Dynamics algorithm repeatedly uses bootstrap to move from one iteration of the branching distributional equation to the next, which dramatically reduces the exponential complexity of the naïve Monte Carlo approach. We present new results guaranteeing the convergence of the Wasserstein distance between the distribution of the pool generated by the algorithm and that of the true attracting endogenous solution.

**Refreshments will be served at 3:00pm in the 3 ^{rd} floor lounge of Hanes Hall**