# Probability Seminar

Monday, February 12, 2018 - 2:30pm to 3:30pm
LOW 101

We study solutions to the stochastic fixed point equation X = AX+B when the coefficients are nonnegative and B
is an inverse exponential decay'' IED random variable.
We provide theorems on the left tail of X which complement  well-known tail results of Kesten and Goldie. We generalize our results to ARMA processes with nonnegative coefficients whose noise terms are from the IED class.
We describe the lower envelope for these ARMA processes. Joint work with Krzysztof Burdzy.

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