Keilson's theorem and the mysteries of time attribution

par Gerold Alsmeyer (Univertät Münster)

vendredi 27 mars 2026, 10:30 → 11:30 Europe/Paris

E2 1180 (Tours)

Keilson's theorem states that the time to absorption in $N$ of
a birth-death process on $\{0,\ldots,N\}$ with starting point 0 is the
sum of $N$ independent exponential random variables with parameters
given by the absolute values of the nonzero eigenvalues of the
generator. Although easy to state and not too difficult to prove by
means of Laplace transforms, the intriguing and somewhat mysterious
aspect of the result is how the time given by the exponential variables
can be attributed. The answer was provided by Miclo and Diaconis by a
clever intertwinement of the given process with a certain dual. I will
speak about this and also about two other decompositions, again
involving exponential random variables.