Stochastic Analysis Seminar
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Mon, 15/01/2007 14:15 |
Dr Peter Fritz (University of Cambridge) |
Stochastic Analysis Seminar  |
DH 3rd floor SR |
| 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.) | |||
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Mon, 15/01/2007 15:45 |
Dr Saadia Ghazali (Imperial College London) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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. | |||
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Mon, 22/01/2007 00:00 |
Stochastic Analysis Seminar |
St Anne's College | |
| /notices/events/special/fluids/ | |||
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Mon, 29/01/2007 14:15 |
Prof Ana Bela Cruzeiro (University of Lisbon) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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). | |||
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Mon, 29/01/2007 15:45 |
Dr Jiang Lung Wu (University of Wales, Swansea) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We consider Burgers type nonlinear SPDEs with L | |||
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Mon, 05/02/2007 14:15 |
Prof Jean Mairesse (University of Paris VII) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 05/02/2007 15:45 |
Prof Francis Comets (University of Paris VII) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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. | |||
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Mon, 12/02/2007 14:15 |
Prof Andreas Eberle (University of Bonn) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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. | |||
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Mon, 12/02/2007 15:45 |
Prof Paul Malliavin (University of Paris XI) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 19/02/2007 14:15 |
Prof Jean Dominique Deuschel (Technical University of Berlin) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 19/02/2007 15:45 |
Dr Peter Topping (University of Warwick) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 26/02/2007 14:15 |
Prof Yves Le Jan (University of Paris XI) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We will see how Dynkin's isomorphism emerges from the "loop soup" introduced by Lawler and Werner. | |||
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Mon, 26/02/2007 15:45 |
Mr Lihu Xu (Imperial College, London) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We start from the stochastic Ising model(or Glauber Dynamics) and have a short review of some important topics in Particle Systems such as ergodicity, convergence rates and so on. Then an abstract nonlinear model will be introduced by an evolution differential equation. We will build the existence and uniqueness theorem, and give some nice properties such as convergence exponentially and monotonicity for the abstract systems. To apply our abstract theory, we will study a family of nonlinear interacting particle systems generalized from Glauber Type Dynamics(we call them nonlinear Glauber Type Dynamics) and prove that such generalization can be done in infinitely many ways. For nonlinear Glauber Type Dynamics, we have two interesting inequalities related to Gibbs measures. Finally, we will concentrate on one specific nonlinear dynamics, and provide the relation between nonlinear system and the linear one, and that between Gibbs measures and tangent functionals to a nonlinear transfer operator. | |||
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Mon, 05/03/2007 14:15 |
Dr Vincent Beffara (ENS Lyon) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We present a link between polymer pinning by a columnar defect in a random medium and a particular model of interacting particles on the line, related to polynuclear growth. While the question of whether an arbitrarily small intensity for the defect always results in pinning is still open, in a 'randomized' version of the model, which is closely related to the zero-temperature Glauber dynamics of the Ising model, we are able to obtain explicit results and a complete understanding of the process. This is joint work with Vladas Sidoravicius and Maria Eulalia Vares. | |||
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Mon, 05/03/2007 15:45 |
Dr Simon Harris (University of Bath) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
