14:15
Forthcoming events in this series
14:15
15:45
Quasi-invariance of the canonical brownian measure on the diffeomorphism group of the circle
14:15
Stability of sequential Markov chain Monte Carlo methods
Abstract
Sequential Monte Carlo Samplers are a class of stochastic algorithms for
Monte Carlo integral estimation w.r.t. probability distributions, which combine
elements of Markov chain Monte Carlo methods and importance sampling/resampling
schemes. We develop a stability analysis by functional inequalities for a
nonlinear flow of probability measures describing the limit behaviour of the
methods as the number of particles tends to infinity. Stability results are
derived both under global and local assumptions on the generator of the
underlying Metropolis dynamics. This allows us to prove that the combined
methods sometimes have good asymptotic stability properties in multimodal setups
where traditional MCMC methods mix extremely slowly. For example, this holds for
the mean field Ising model at all temperatures.
15:45
Fluctuations of the front in a one dimensional growth model
Abstract
We report on two joint works with Jeremy Quastel and Alejandro Ramirez, on an
interacting particle system which can be viewed as a combustion mechanism or a
chemical reaction.
We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in
which $Y$ particles do not move while $X$ particles move as independent
continuous time, simple symmetric random walks. $Y$ particles are transformed
instantaneously to $X$ particles upon contact.
We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the
right of the origin, and define a class of configurations of the $X$ particles
to the left of the origin having a finite $l^1$ norm with a specified
exponential weight. Starting from any configuration of $X$ particles to the left
of the origin within such a class, we prove a central limit theorem for the
position of the rightmost visited site of the $X$ particles.
14:15
15:45
Burgers type nonlinear stochastic equations involving Levy Generators in one space variable
Abstract
We consider Burgers type nonlinear SPDEs with L
14:15
Diffusions on the volume preserving diffeomorphisms group and hydrodynamics equations
Abstract
We follow Arnold's approach of Euler equation as a geodesic on the group of
diffeomorphisms. We construct a geometrical Brownian motion on this group in the
case of the two dimensional torus, and prove the global existence of a
stochastic perturbation of Euler equation (joint work with F. Flandoli and P.
Malliavin).
Other diffusions allow us to obtain the deterministic Navier-Stokes equation
as a solution of a variational problem (joint work with F. Cipriano).
00:00
15:45
The Global Error in Weak Approximations of Stochastic Differential Equations
Abstract
In this talk, the convergence analysis of a class of weak approximations of
solutions of stochastic differential equations is presented. This class includes
recent approximations such as Kusuoka's moment similar families method and the
Lyons-Victoir cubature on Wiener Space approach. It will be shown that the rate
of convergence depends intrinsically on the smoothness of the chosen test
function. For smooth functions (the required degree of smoothness depends on the
order of the approximation), an equidistant partition of the time interval on
which the approximation is sought is optimal. For functions that are less smooth
(for example Lipschitz functions), the rate of convergence decays and the
optimal partition is no longer equidistant. An asymptotic rate of convergence
will also be presented for the Lyons-Victoir method. The analysis rests upon
Kusuoka-Stroock's results on the smoothness of the distribution of the solution
of a stochastic differential equation. Finally, the results will be applied to
the numerical solution of the filtering problem.
14:15
Differential Equations Driven by Gaussian Signals
Abstract
We consider multi-dimensional Gaussian processes and give a novel, simple and
sharp condition on its covariance (finiteness of its two dimensional rho-variation,
for some rho <2) for the existence of "natural" Levy areas and higher iterated
integrals, and subsequently the existence of Gaussian rough paths. We prove a
variety of (weak and strong) approximation results, large deviations, and
support description.
Rough path theory then gives a theory of differential equations driven by
Gaussian signals with a variety of novel continuity properties, large deviation
estimates and support descriptions generalizing classical results of
Freidlin-Wentzell and Stroock-Varadhan respectively.
(Joint work with Nicolas Victoir.)
15:45
SPDEs of second order in time and their sample paths
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/sanz-sole.shtml
14:15
Duistermaat-Heckman measure for Coxeter groups
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/o
15:45
Mean-Reversion versus Random Walk in Energy Commodity Prices
Abstract
\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\stochastic-analysis\mt06\geman.shtml
14:15
Branching Markov Chains
Abstract
\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\stochastic-analysis\mt06\gantert.shtml
15:45
Randon tilings and random matrices
Abstract
\\common\dfs\htdocs\www\maintainers\reception\enb\abstracts\stochastic-analysis\mt06\johansson
14:15
Optimal stopping of one-dimensional Ito diffusions with applications to the timing of investment decisions
15:45
Pathwise stochastic optimal control
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/rogers.shtml
14:15
Applications of ransom matrix theory to statistics of the Riemann zeta function
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/snaith.shtml
15:45
Concentration inequalities and particle approximation of a mean field model
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/bolley.shtml
14:15
The ensemble Kalman filter: a state estimation method for hazardous weather prediction
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/dance.shtml
15:45
Random walks in Dirichlet environment and hypergeometric integrals
14:15
Dual Nonlinear Filters and Entropy Production
Abstract
15:45
5x+1: how many go down?
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/volkov.shtml
14:15
15:45
Random walk on the incipient infinite cluster for oriented percolation
Abstract
\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\stochastic-analysis\mt06\barlow