Mon, 22 Oct 2007
14:15
Oxford-Man Institute

Slow energy dissipation in anharmonic chains

Dr. Martin Hairer
(University of Warwick)
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.

Mon, 11 Jun 2007
14:15
DH 3rd floor SR

Monte Carlo Markoc Chain Methods in Infinite Dimensions

Professor Andrew Stuart
(University of Warwick)
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.

 

Mon, 22 May 2006
14:15
DH 3rd floor SR

Exotic couplings of Brownian motion

Prof Wilfrid Kendall
(University of Warwick)
Abstract

/notices/events/abstracts/stochastic-analysis/tt06/Kendall.shtml

Mon, 13 Jun 2005
15:45
DH 3rd floor SR

On some first passage problems for 1/2 semi-stable Markov processes enjoying the time-inversion property

Dr Larbi Alili
(University of Warwick)
Abstract

We review the analytic transformations allowing to construct standard bridges from a semistable Markov process, with indec 1/2, enjoying the time inversion property. These are generalized and some of there properties are studied. The new family maps the space of continuous real-valued functions into a family which is the topic of our focus. We establish a simple and explicit formula relating the distributions of the first hitting times of each of these by the considered semi-stable process

Mon, 08 Nov 2004
15:45
DH 3rd floor SR

Result of PhD thesis which is a large deviation result for diffusions under the influence of a strong drift

Dr Jochen Voss
(University of Warwick)
Abstract

We present a large deviation result for the behaviour of the

end-point of a diffusion under the influence of a strong drift. The rate

function can be explicitely determined for both attracting and repelling

drift. It transpires that this problem cannot be solved using

Freidlin-Wentzel theory alone. We present the main ideas of a proof which

is based on the Girsanov-Formula and Tauberian theorems of exponential type.

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