Stochastic Analysis Seminar
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Mon, 23/04/2007 14:15 |
Prof Thomas Zastawniak (University of York) |
Stochastic Analysis Seminar  |
DH 3rd floor SR |
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Mon, 23/04/2007 15:45 |
Dr Erika Hausenblas |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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First I will introduce Poisson random measures and their connection to Levy processes. Then SPDE |
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Mon, 30/04/2007 14:15 |
Dr Nadia Sidorova (University of Bath) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We study the parabolic Anderson problem, i.e., the heat equation on the d-dimentional integer lattice with independent identically distributed random potential and localised initial condition. Our interest is in the long-term behaviour of the random total mass of the unique non-negative solution, and we prove the complete localisation of mass for potentials with polynomial tails. | |||
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Mon, 30/04/2007 15:45 |
Dr Amanda Turner (University of Cambridge) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Diffusion limited aggregation (DLA) is a random growth model which was originally introduced in 1981 by Witten and Sander. This model is prevalent in nature and has many applications in the physical sciences as well as industrial processes. Unfortunately it is notoriously difficult to understand, and only one rigorous result has been proved in the last 25 years. We consider a simplified version of DLA known as the Eden model which can be used to describe the growth of cancer cells, and show that under certain scaling conditions this model gives rise to a limit object known as the Brownian web. | |||
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Mon, 07/05/2007 14:15 |
Liza Jones (Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 07/05/2007 15:45 |
Professor Xuerong Mao (University of Strathclyde) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Relatively little is known about the ability of numerical methods for stochastic differential equations (SDE |
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Mon, 14/05/2007 14:15 |
Dr Oliver Riordan (University of Cambridge (DPMS)) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Recently, comparison with branching processes has been used to determine the asymptotic behaviour of the diameter (largest graph distance between two points that are in the same component) of various sparse random graph models, giving results for $G(n,c/n)$ as special cases. In ongoing work with Nick Wormald, we have studied $G(n,c/n)$ directly, obtaining much stronger results for this simpler model. | |||
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Mon, 14/05/2007 15:45 |
Professor Zhi-Ming Ma (Chinese Academy of Sciences, Beijing) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The talk is based on my recent joint work with Zhechun Hu and Wei Sun. We consider a nonlinear filtering problem for general right continuous Markov processes associated with semi-Dirichlet forms. We show that in our general setting the filtering processes satisfy also DMZ (Duncan-Mortensen-Zakai) equation. The uniqueness of the solutions of the filtering equations are verified through their Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. We investigate further the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes. | |||
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Mon, 21/05/2007 14:15 |
Prof Brian Davies (Kings College, London) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 21/05/2007 15:45 |
Greg Gyurko (Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The "Cubature on Wiener space" algorithm can be regarded as a general approach to high order weak approximations. Based on this observation we will derive many well known weak discretisation schemes and optimise the computational effort required for a given accuracy of the approximation. We show that cubature can also help to overcome some stability difficulties. The cubature on Wiener space algorithm is frequently combined with partial sampling techniques and we outline an extension to these methods to reduce the variance of the samples. We apply the extended method to examples arising in mathematical finance. Joint work of G. Gyurko, C. Litterer and T. Lyons | |||
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Mon, 28/05/2007 14:15 |
Professor Dominique Bakry (Université de Toulouse) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Gradient bounds are a very powerful tool to study heat kernel measures and regularisation properties for the heat kernel. In the elliptic case, it is easy to derive them from bounds on the Ricci tensor of the generator. In recent years, many efforts have been made to extend these bounds to some simple examples in the hypoelliptic situation. The simplest case is the Heisenberg group. In this talk, we shall discuss some recent developments (due to H.Q. Li) on this question, and give some elementary proofs of these bounds. | |||
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Mon, 28/05/2007 15:45 |
Mr Anthony Metcalfe (University of Cork, Ireland) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| A dimer configuration of a graph is a subset of the edges, such that every vertex is contained in exactly one edge of the subset. We consider dimer configurations of the honeycomb lattice on the cylinder, which are known to be equivalent to configurations of interlaced particles. Assigning a measure to the set of all such configurations, we show that the probability that particles are located in any subset of points on the cylinder can be written as a determinant, i.e. that the process is determinantal. We also examine Markov chains of interlaced particles on the circle, with dynamics equivalent to RSK. | |||
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Mon, 04/06/2007 14:15 |
Dr Qingyang Guan (Imperial College, London) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Schramm Loewner Evolutions (SLE) are random planar curves (if κ ≤ 4) or growing compact sets generated by a curve (if κ > 4). We consider more general L | |||
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Mon, 04/06/2007 15:45 |
Dr. Massimiliano Gubinelli (Universite Paris-Sud) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| I will describe some applications of the main techniques of rough paths theory to problems not related to SDE | |||
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Mon, 11/06/2007 14:15 |
Professor Andrew Stuart (University of Warwick) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| 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. | |||
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Mon, 11/06/2007 15:45 |
Professor Aline Kurtzmann (Universite de Neuchatel) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Self-interacting diffusions are solutions to SDEs with a drift term depending on the process and its normalized occupation measure $\mu_t$ (via an interaction potential and a confinement potential): $$\mathrm{d}X_t = \mathrm{d}B_t -\left( \nabla V(X_t)+ \nabla W*{\mu_t}(X_t) \right) \mathrm{d}t ; \mathrm{d}\mu_t = (\delta_{X_t} - \mu_t)\frac{\mathrm{d}t}{r+t}; X_0 = x,\,\ \mu_0=\mu$$ where $(\mu_t)$ is the process defined by $$\mu_t := \frac{r\mu + \int_0^t \delta_{X_s}\mathrm{d}s}{r+t}.$$ We establish a relation between the asymptotic behaviour of $\mu_t$ and the asymptotic behaviour of a deterministic dynamical flow (defined on the space of the Borel probability measures). We will also give some sufficient conditions for the convergence of $\mu_t$. Finally, we will illustrate our study with an example in the case $d=2$. | |||
