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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

7 votes
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How long for a simple random walk to exceed $\sqrt{T}$?

For a Brownian motion, Novikov finds an explicit expression for any real moments (positive and negative) of the random variable $(\tau(a,b,c)+c)$, where $$ \tau(a,b,c) = \inf(t \geq 0, W(t) \leq -a +b …
Louigi Addario-Berry's user avatar
2 votes

is there an interpretation to the inverse of $I-M$ in multitype branching process, where $M$...

In general, if $M$ was the transition matrix (infinitesimal generator) of a Markov chain , this functional would be called called the resolvent. Perhaps you already knew this; if not, you could look a …
Louigi Addario-Berry's user avatar