Event Detail

Event Type: 
Analysis Seminar
Monday, November 2, 2015 - 12:00 to 13:00
Kidder 356

Speaker Info

Graduate Student

Let \((B_t)\) be a d-dimensional Brownian motion, and consider the stochastic
differential equation \(dX_t = x + B_t + \int_0^t b(X_s) ds\) where \(b(x)\) is a
gradient; that is \(b(x) = grad (V(x))\) for some potential function \(V\). The
Markov process so generated provides a semigroup operator, \(E[f(X_t) | X_0]\),
on distributions on euclidean space. There exist criteria to discern
whether there is a nontrivial invariant distribution which the system tends
to over time, i.e. tests for ergodicity. Under some mild conditions, the
common class of operators above does exhibit ergodic behavior. In this talk
we follow the work of Ganidis and discuss the question of how quickly the
distributions approach their invariant distribution. We find that the
growth rate of \(V\) will imply bounds on the rate of convergence.