Stochastic Analysis Seminar
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Mon, 25/04/2005 14:15 |
Dr Keisuke Hara (Ritsumeikan University Japan) |
Stochastic Analysis Seminar  |
DH 3rd floor SR |
| I will show rough path estimates for smooth L^p functions whose derivatives are in L^q. The application part related to (linear or nonlinear) Fourier analysis will be also discussed. | |||
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Mon, 25/04/2005 15:45 |
Professor Francesco Russo (Université de Paris 13) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We aim at presenting some aspects of stochastic calculus via regularization in relation with integrator processes which are generally not semimartingales. Significant examples of those processes are Dirichlet processes, Lyons-Zheng processes and fractional (resp. bifractional) Brownian motion. A Dirichlet process X is the sum of a local martingale M and a zero quadratic variation process A. We will put the emphasis on a generalization of Dirichlet processes. A weak Dirichlet process is the sum of local martingale M and a process A such that [A,N] = 0 where N is any martingale with respect to an underlying filtration. Obviously a Dirichlet process is a weak Dirichlet process. We will illustrate partly the following application fields. Analysis of stochastic integrals related to fluidodynamical models considered for instance by A. Chorin, F. Flandoli and coauthors... Stochastic differential equations with distributional drift and related stochastic control theory. The talk will partially cover joint works with M. Errami, F. Flandoli, F. Gozzi, G. Trutnau. | |||
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Mon, 02/05/2005 14:15 |
Dr Feng Yu (University of British Columbia) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We study diploid branching particle models and its behaviour when rapid stirring, i.e. rapid exchange of particles between neighbouring spatial sites, is added to the interaction. The particle models differ from the ``usual'' models in that they all involve two types of particles, male and female, and branching can only occur when both types of particles are present. We establish the existence of nontrivial stationary distributions for various models when birth rates are sufficiently large. | |||
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Mon, 02/05/2005 15:45 |
Dr David Croydon (Mathematical Institute Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The estimation of heat kernels has been of much interest in various settings. Often, the spaces considered have some kind of uniformity in the volume growth. Recent results have shown that this is not the case for certain random fractal sets. I will present heat kernel bounds for spaces admitting a suitable resistance form, when the volume growth is not uniform, which are motivated by these examples. | |||
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Mon, 09/05/2005 14:15 |
Professor G. R. Grimmett (University of Cambridge) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 09/05/2005 15:45 |
Professor Thierry Levy (ENS Paris) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The Yang-Mills energy is a non-negative functional on the space of connections on a principal bundle over a Riemannian manifold. At a heuristical level, this energy determines a Gibbs measure which is called the Yang-Mills measure. When the manifold is a surface, a stochastic process can be constructed - at least in two different ways - which is a sensible candidate for the random holonomy of a connection distributed according to the Yang-Mills measure. This process is constructed by using some specifications given by physicists of its distribution, namely some of its finite-dimensional marginals, which of course physicists have derived from the Yang-Mills energy, but by non-rigorous arguments. Without assuming any familiarity with this stochastic process, I will present a large deviations result which is the first rigorous link between the Yang-Mills energy and the Yang-Mills measure. | |||
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Mon, 16/05/2005 14:15 |
Dr. Martin Barlow (University of British Columbia) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| It is now known that the overall behaviour of a simple random walk (SRW) on supercritical (p>p_c) percolation cluster in Z^d is similiar to that of the SRW in Z^d. The critical case (p=p_c) is much harder, and one needs to define the 'incipient infinite cluster' (IIC). Alexander and Orbach conjectured in 1982 that the return probability for the SRW on the IIC after n steps decays like n^{2/3} in any dimension. The easiest case is that of trees; this was studied by Kesten in 1986, but we can now revisit this problem with new techniques. | |||
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Mon, 16/05/2005 15:45 |
Dr Michael Caruana (Mathematical Institute, Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We show that the solutions of stochastic differential equations converge in the rough path metric as the coefficients of these equations converge in a suitable lipschitz norm. We then use this fact to obtain results about differential equations driven by the Brownian rough path. | |||
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Mon, 23/05/2005 14:15 |
Dr Christophe Sabot (Université Paris 6) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Random Walks in Dirichlet Environment play a special role among random walks in random environments since the annealed law corresponds to the law of an edge oriented reinforced random walks. We will give few results concerning the ballistic behaviour of these walks and some properties of the asymptotic velocity. We will also compare the behaviour of these walks with general random walks in random environments in the limit of small disorder | |||
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Mon, 23/05/2005 15:45 |
Dr. Jiri Cerny (Weierstrass Institute Berlin) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The aging of spin-glasses has been of much interest in the last decades. Since its explanation in the context of real spin-glass models is out of reach, several effective models were proposed in physics literature. In my talk I will present how aging can be rigorously proved in so called trap models and what is the mechanism leading to it. In particular I will concentrate on conditions leading to the fact that one of usual observables used in trap models converges to arc-sine law for Levy processes. | |||
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Mon, 30/05/2005 14:15 |
Professor Gregory Miermont (Universite d'Orsay France) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| In recent years, the use of random planar maps as discretized random surfaces has received a considerable attention in the physicists community. It is believed that the large-scale properties, or the scaling limit of these objects should not depend on the local properties of these maps, a phenomenon called universality. By using a bijection due to Bouttier-di Francesco-Guitter between certain classes of planar maps and certain decorated trees, we give instances of such universality phenomenons when the random maps follow a Boltzmann distribution where each face with degree $2i$ receives a nonnegative weight $q(i)$. For example, we show that under certain regularity hypothesis for the weight sequence, the radius of the random map conditioned to have $n$ faces scales as $n^{1/4}$, as predicted by physicists and shown in the case of quadrangulations by Chassaing and Schaeffer. Our main tool is a new invariance principle for multitype Galton-Watson trees and discrete snakes. | |||
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Mon, 30/05/2005 15:45 |
Dr Andreas E. Kyprianou (Heriot Watt University Edinburgh) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We obtain a new identity giving a quintuple law of overshoot, time of overshoot, undershoot, last maximum, and time of last maximum of a general Levy process at ?rst passage. The identity is a simple product of the jump measure and its ascending and descending bivariate renewal measures. With the help of this identity, we consider applications for passage problems of stable processes, recovering and extending results of V. Vigon on the bivariate jump measure of the ascending ladder process of a general Levy process and present some new results for asymptotic overshoot distributions for Levy processes with regularly varying jump measures. (Parts of this talk are based on joint work with Ron Doney and Claudia Kluppelberg) | |||
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Mon, 06/06/2005 14:15 |
Dr Phillip Yam (Mathematical Institute, Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 06/06/2005 15:45 |
Professor Jean-Francois Le Gall (Université Paris 5) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 13/06/2005 14:15 |
John Moriarty (University College Cork) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| When two single server queues have the same arrivals process, this is said to be a `fork-join queue'. In the case where the arrivals and service processes are Brownian motions, the queue lengths process is a reflecting Brownian motion in the nonnegative orthant. Tan and Knessl [1996] have given a simple explicit formula for the stationary distribution for this queueing system in a symmetric case, which they obtain as a heavy traffic limit of the classical discrete model. With this as a starting point, we analyse the Brownian model directly in further detail, and consider some related exit problems. | |||
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Mon, 13/06/2005 15:45 |
Dr Larbi Alili (University of Warwick) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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 | |||
