26 research outputs found
Small Deviations of Smooth Stationary Gaussian Processes
We investigate the small deviation probabilities of a class of very smooth
stationary Gaussian processes playing an important role in Bayesian statistical
inference. Our calculations are based on the appropriate modification of the
entropy method due to Kuelbs, Li, and Linde as well as on classical results
about the entropy of classes of analytic functions. They also involve
Tsirelson's upper bound for small deviations and shed some light on the limits
of sharpness for that estimate
Small deviations of iterated processes in space of trajectories
We derive logarithmic asymptotics of probabilities of small deviations for
iterated processes in the space of trajectories. We find conditions under which
these asymptotics coincide with those of processes generating iterated
processes. When these conditions fail the asymptotics are quite different
Efficient low-order approximation of first-passage time distributions
We consider the problem of computing first-passage time distributions for
reaction processes modelled by master equations. We show that this generally
intractable class of problems is equivalent to a sequential Bayesian inference
problem for an auxiliary observation process. The solution can be approximated
efficiently by solving a closed set of coupled ordinary differential equations
(for the low-order moments of the process) whose size scales with the number of
species. We apply it to an epidemic model and a trimerisation process, and show
good agreement with stochastic simulations.Comment: 5 pages, 3 figure