Research page of Matthias Winkel

Contact details

Email: winkel@stats.ox.ac.uk
Phone: +44 1865 2 72875
Address: Department of Statistics, 1 South Parks Road, Oxford OX1 3TG, UK
URL: http://www.stats.ox.ac.uk/~winkel/indexe.html

Research interests: stochastic processes and applications

Main interests

Lévy processes, subordinators, time changes
Random trees and forests, branching processes, superprocesses
Exchangeability

I'm looking for Ph.D. students interested in my main research interests. Feel free to send me an email if you'd like to find out more about what's behind these topics. Briefly, my aim is to follow a probabilistic approach guided by heuristic arguments and pictures, but some advanced probability theory and analytical tools are required to then establish results rigorously. This is not meant to sound like a list of prerequisites but you should expect to spend a good proportion of your time, particularly initially, doing guided reading of selected parts of the literature to extend your tool kit.

Side interests

Stochastic Loewner Evolutions
Burgers turbulence model, sticky particle systems
Econometric models, foreign exchange markets, stock markets, stochastic volatility
Insurance risk models, actuarial mathematics

I don't take on Ph.D. students interested in my side interests except in joint supervision. I have had two such students jointly with Neil Shephard and Bent Nielsen, both in the Economics Group of Nuffield College, but I'm open to other joint supervisions.

Collaborators and other contacts

Collaborators: Ole Barndorff-Nielsen (Aarhus), Thomas Duquesne (Paris 6), Bénédicte Haas (Paris-Dauphine), Grégory Miermont (Orsay), Jim Pitman (Berkeley), Neil Shephard (Oxford), Qingyang Guan (Chinese Academy of Sciences, Beijing)
Former Ph.D. students: Almut Veraart (jointly supervised with Neil Shephard, completed in 2007, now in Aarhus), Di Kuang (jointly supervised with Bent Nielsen, completed in 2008, now at Aon), Bo Chen (completed in 2009)
Ph.D. students: John Cao, Yu Xue
Former supervisors: Gerold Alsmeyer (Münster), Ron Doney (Manchester), Jean Bertoin (Paris), Ole Barndorff-Nielsen (Aarhus)
Other scientific contacts: Nick Bingham (Sheffield), Alison Etheridge (Oxford), Steve Evans (Berkeley), Christina Goldschmidt (Oxford), Ben Hambly (Oxford), Alexander Holroyd (Vancouver), Niels Jacob (Swansea), Jean-François Le Gall (Orsay), Yves Le Jan (Orsay), Terry Lyons (Oxford), Philippe Marchal (Paris), James Martin (Oxford), Bent Nielsen (Oxford), Gesine Reinert (Oxford), Rene Schilling (Dresden), Wendelin Werner (Orsay), Marc Yor (Paris)
Contacts at the industry interface: Matthew Eagle (Aon), Paul King (Mercer), Jens Perch Nielsen (Codan)

Publications with links to pdf files (preprint versions, where appropriate)

Winkel, M.: Burgers turbulence initialized by a regenerative impulse. Stoch. Proc. Appl. 93, 241-268 (2001)
Winkel, M.: Right inverses of non-symmetric Lévy processes. Ann. Prob. 30, 382-415 (2002)
Winkel, M.: Limit clusters in the inviscid Burgers turbulence with certain random initial velocities. J. Stat. Phys. 107, 893-917 (2002)
Winkel, M.: Electronic foreign exchange markets and passage events of independent subordinators. J. Appl. Prob. 42, 138-152 (2005)
Winkel, M.: The recovery problem for time-changed Lévy processes. Preprint
Pitman, J. and Winkel, M.: Growth of the Brownian forest. Ann. Prob. 33, 2188-2211 (2005)
Barndorff-Nielsen, O.E., Shephard, N. and Winkel, M.: Limit theorems for multipower variation in the presence of jumps. Stoch. Proc. Appl. 116, 796-806 (2006)
Duquesne, T. and Winkel, M.: Growth of Lévy trees. Probability Theory and Related Fields 139, no. 3-4, 313-371 (2007)
Haas, B., Miermont, G., Pitman, J. and Winkel, M.: Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. Ann. Prob. 36, No. 5, 1790-1837 (2008)
Guan, Q.-Y. and Winkel, M.: SLE and alpha-SLE driven by Lévy processes. Ann. Prob. 36, No. 4, 1221-1266 (2008)
McCullagh, P., Pitman, J. and Winkel, M.: Gibbs fragmentation trees. Bernoulli 14(4), 988-1002 (2008)
Haas, B., Pitman, J. and Winkel, M.: Spinal partitions and invariance under re-rooting of continuum random trees.. Ann. Prob. 37, No. 4, 1381-1411 (2009)
Pitman, J. and Winkel, M.: Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions. Ann. Prob. 37, No. 5, 1999-2041 (2009)
Chen, B., Ford, D. and Winkel, M.: A new family of Markov branching trees: the alpha-gamma model. Elec. J. Prob. 14, 400-430 (2009)
Veraart, A. and Winkel, M.: Time change. to appear in Encyclopedia of Quantitative Finance, ed. R. Cont, Wiley (2010)
Chen, B. and Winkel, M.: Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees. arXiv:0911.5647 submitted (2009)
Savov, M. and Winkel, M.: Right inverses of Lévy processes: the excursion measure in the general case. Elec. C. Prob. 15, 572-584 (2010)
Cao, X. and Winkel, M.: Growth of Galton-Watson trees: immigration and lifetimes. arXiv:1004.3061 submitted (2010)

Brief version of my curriculum vitae

M.Sc. (Manchester, 1998), Diplom (Münster, 1999), Ph.D. (Paris, 2001)
04/01-03/02 Pre- and postdoctoral stay at the University of Aarhus
since 04/02 Departmental Lecturership at the Department of Statistics, University of Oxford, 10/02-12/06 Associate Membership at Nuffield College Oxford, 04/07-09/09 College Lecturership at St Catherine's College Oxford, since 02/03 College Lecturership at Trinity College Oxford