recursive functions

Hi i have been asked to find unconditional expectations and then a recursive relation. I think I have started well but i am confused at how the recursive relation is made up. this is then to be used with a GARCH model i am working on. details of question: d(t) = mu + sigma(t)Z(t)...

So I've been getting into concepts like the Library of Babel and infinite monkey theorem, and have been trying to work out how to calculate the probability that a given string of text contains a particular substring at least once. To simplify things, I'm going to talk about numerals. Suppose my...