15:45
Phase diagram for a stochastic reaction diffusion equation.
Abstract
The system
u_t = Delta u + buv - cu + u^{1/2} dW
v_t = - uv
models the evolution of a branching population and its usage of a non-renewable resource.
A phase diagram in the parameters (b,c) describes its long time evolution.
We describe this, including some results on asymptotics in the phase diagram for small and large values of the parameters.
16:00
14:15
Slow energy dissipation in anharmonic chains
Abstract
We study the dynamic of a very simple chain of three anharmonic oscillators with linear nearest-neighbour couplings. The first and the last oscillator furthermore interact with heat baths through friction and noise terms. If all oscillators in such a system are coupled to heat baths, it is well-known that under relatively weak coercivity assumptions, the system has a spectral gap (even compact resolvent) and returns to equilibrium exponentially fast. It turns out that while it is still possible to show the existence and uniqueness of an invariant measure for our system, it returns to equilibrium much slower than one would at first expect. In particular, it no longer has compact resolvent when the potential of the oscillators is quartic and the spectral gap is destroyed when it grows even faster.
14:15
Monte Carlo Markoc Chain Methods in Infinite Dimensions
Abstract
A wide variety of problems arising in applications require the sampling of a
probability measure on the space of functions. Examples from econometrics,
signal processing, molecular dynamics and data assimilation will be given.
In this situation it is of interest to understand the computational
complexity of MCMC methods for sampling the desired probability measure. We
overview recent results of this type, highlighting the importance of measures
which are absolutely continuous with respect to a Guassian measure.
15:45
15:45
Multi-scaling of the $n$-point density function for coalescing Brownian motions
Abstract
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14:15
Exotic couplings of Brownian motion
Abstract
/notices/events/abstracts/stochastic-analysis/tt06/Kendall.shtml
14:15
17:00