Tuesday Lunch Meetings
The meetings are on Tuesdays at 12:00 in Aud. 10 at HCØ.
05/05/2009: Bent Jørgensen
Title: Power Asymptotics for Self-Similar Stochastic Systems Generated by Exponential Tilting
Abstract: We introduce a notion of self-similarity for stochastic systems, which are families of random measures on R^{d}, and explore the connection with Tweedie power asymptotics, where Hougaard Lévy processes appear in the limit. More generally, we (attempt to) show a Lamperti-type convergence theorem, where a new type of fractional self-similar stochastic systems appear in the limit. Such systems satisfy the so-called Taylor's power law for the variance-to-mean relation of a spatial distribution, known to hold empirically for many animal populations, while exhibiting a form of long-range dependence found in such population networks. We also speculate about extending the Lamperti transformation to the new setting, and its possible use for defining Ornstein-Uhlenbeck versions of Hougaard processes.
04/11/2008: Jesper Lund Pedersen
Title: First passage times and strong Markov property
Abstract: An equation derived from strong Markov property - e.g. for linear diffusions - will be used to compute distributional properties of first passage times based on the law of the underlying process. The distributional properties are: Laplace transform, hitting probability, expectation and reflection principle.
02/09/2008: Bo Markussen
Title: Laplace approximation of transition densities - a functional approach
Abstract: The solution to a SDE observed at given time point can be seen as a functional of the driving Brownian motion. Using various tricks we implement the Laplace approximation of transition densities posed as Brownian expectations. A usefull side product is the rigorous introduction of maximum a posteriori estimation of SDEs. Currently, the method is implemented in R for one-dimensional discretely observed SDEs. But in principle the method is numerically operational for partial and discretely observed multivariate SDEs.
The talk is based on this paper.
10/06/2008: Helle Sørensen
Title: Goodness of fit based on downsamples
Coauthors: Julie Lyng Forman and Bo Markussen
Abstract: We develop a goodness of fit test based on comparison of distributions for different sampling frequencies. More specifically the test compares parameter estimates, based on estimating functions, for downsamples of the data. We prove asymptotic results for models for stationary and ergodic processes. Specifically we investigate a test for a linear drift hypothesis. Simulations indicate that the test is quite powerful in detecting non-Markovian deviations from the hypothesis, thus it is a good supplement to existing goodness of fit tests.
20/05/2008: Martin Jacobsen
Title: Exit time problems and the partial eigenfunction method.
Abstract: the use of partial eigenfunctions has proven a very effective technique for finding Laplace transforms of exit times from intervals of e.g certain Markov processes with jumps. Rather than present the more general results that have been obtained, the talk will focus on a particularly simple special case, which can be used to illustrate how the method works and also to give examples of the type of new problems it would be nice to solve.
04/03/2008: Theis Rasmus Lange
Title: Addressing the IGARCH Puzzle.
Coauthor: Anders Tolver.