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An EMMaPS workshop: Stochastic Models and Numerical Methods
11th May (Wed) 2011, Department of Mathematics, University of Leicester
This one-day workshop is partly sponsored by the London Mathematical Society within the East Midlands Mathematical Physics Seminar (EMMaPS) series.
Additional funding is provided by Department of Mathematics, University of Leicester.
Date: 11th May (Wed) 2011
Registration Fees: Free; Everyone is very welcome!
Program:
10:30-11:00 : Registration / Tea and Coffee
11:00-11:55 : Anastasia Papavasiliou (University of Warwick)
12:00-13:30 : Lunch
13:30-14:25 : Ray Kawai (University of Leicester)
14:30-15:25 : Jochen Voss (University of Leeds)
15:30-15:50 : Tea and Coffee
15:50-16:45 : Mike Giles (University of Oxford)
Title and Abstract:
Anastasia Papavasiliou (University of Warwick)
Title: Applications of the theory of rough paths to statistics
Abstract: I will discuss the problem of statistical inference for differential equations driven by rough paths (RDEs). First, I will present in detail the method of Moment Matching in the context of RDEs. Then, I will go on to discuss different types of estimators. Note that RDEs are very general and, apart from diffusions, they include non-Markovian models such as differential equations driven by fractional Brownian motion and stochastic delay equations.
Ray Kawai (University of Leicester)
Title: Recent results on local asymptotic normality of stochastic processes under high-frequency sampling
Abstract: I will discuss the local asymptotic normality property and the singularity of the Fisher information appearing in statistical inference for continuous-time stochastic processes of practical interest, such as asset price dynamics in finance and individual animal movement in biology, under high-frequency discrete sampling schemes. Singularity is caused by the scale parameter and the selfsimilarity index, while there exists even a different type of singularity resulting from some redundancy of parameters in the short time framework.
Jochen Voss (University of Leeds)
Title: The Stationary Distribution of Discretised SPDEs
Abstract: I will discuss the problem of how discretisation error affects the solution of a stochastic partial differential
equation (SPDE). In this talk I will focus on finite element discretisation of SPDEs of reaction-diffusion type (in one space dimension). In this situation it transpires that one can give a surprisingly explicit description of the discretisation error; based on this I will derive a result about speed of convergence of the stationary distribution of the discretised SPDE to the correct stationary distribution.
Mike Giles (University of Oxford)
Title: Multilevel Monte Carlo method for elliptic SPDEs
Abstract: The multilevel Monte Carlo is a recently developed method for SDEs in computational finance in which Monte Carlo simulations on different numbers of timesteps are combined to greatly reduce the computational cost of achieving a certain user-specified accuracy. It may be viewed as a recursive control variate strategy, in which the simulation on a coarse level of resolution is used as a control variate for a finer level of resolution.
In this talk, I will discuss joint work with Rob Scheichl and Aretha Teckentrup (Bath) and Andrew Cliffe (Nottingham) on the application of this technique to elliptic SPDEs which arise in the modelling of nuclear waste repositories and oil reservoirs.
Organizers:
Ray Kawai (chair)
Additional Information:
Travel information and campus map can be found here.
For the dedicated few, informal discussions can continue at a local bar and restaurant after the talks.
Last updated: 9 May 2011.
