Oberwolfach Seminar: Statistics for Stochastic Differential Equations

Date

October 16^th - October 22^nd, 2011

Organizers

Susanne Ditlevsen, Copenhagen

Jean Jacod, Paris

Markus Reiß, Berlin

Michael Sørensen, Copenhagen

ID

1142a

Programme

Modeling with stochastic differential equations (SDEs) becomes more and more popular, not only because of the powerful mathematical tools from stochastic analysis, but also because of the increasing availability of measurements and data for dynamical processes, where randomness plays a major role. Therefore also the development of statistical procedures based on SDE models has seen a large rise during the last decade.

We shall introduce Ph.D. students and young postdocs to this fascinating field opening different perspectives. One part will consist of lectures oriented towards biological applications by Susanne Ditlevsen and Michael Sørensen introducing the estimating function methodology, thereby unifying most parametric estimators presented in the literature. Lectures by Jean Jacod and Markus Reiß will study statistical inference for wide (nonparametric) classes of SDEs and semimartingales oriented towards financial applications with topics including low-frequency versus high-frequency observations, stochastic volatility models and microstructure noise. Problem sessions will form a central part of the seminar where students use and develop the theory for concrete examples.

Prerequisites

Stochastic processes and stochastic analysis (at least up to Ito's formula), basic statistical notions (estimation, testing, MLE, moment estimator). Preferably, advanced knowledge in one of those fields (like advanced stochastic analysis, asymptotic statistics, nonparametrics).

Suggested reading

• Iacus, S.M.: Simulation and Inference for Stochastic Differential Equations, Springer, 2008. [a more applied survey on methods and models]
• Karatzas, I. and Shreve, S.E.: Brownian motion and stochastic calculus, 2nd ed, 1991. [classic monograph on stochastic analysis, advanced]
• Øksendal, B.: Stochastic differential equations. An introduction with applications, 6th ed., Universitext, Springer, 2003. [excellent introduction to SDEs]
• Sørensen, M.: Parametric inference for discretely sampled stochastic differential equations. In Andersen, T.G. Davis, R.A., Kreiss, J.-P. and Mikosch, T. (eds.): Handbook of Financial Time Series, Springer, 531-553, preprint under ftp://ftp.econ.au.dk/creates/rp/08/rp08_18.pd [survey paper]

Deadline for applications

August 15^th, 2011

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. The Institute covers accommodation and food. We are pleased that the Carl Friedrich von Siemens Foundation has decided to support the Oberwolfach Seminars from summer 2008 to summer 2013. By this support, travel expenses can be reimbursed up to 200 Euro in average per person. Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent preferably by e-mail (.ps or .pdf file) to:

    Prof. Dr. Dr. h.c. Gert-Martin Greuel
    Universität Kaiserslautern
    Fachbereich Mathematik
    Erwin Schrödingerstr.
    67663 Kaiserslautern, Germany