Personal Website:
+44 1865 615175
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
Invariance principle for the random conductance model
Probability Theory and Related Fields
issue 3-4
volume 156
page 535-580
(1 August 2013)
Convergence of mixing times for sequences of random walks on finite graphs
Electronic Journal of Probability
volume 17
page 1-32
(31 January 2012)
Asymptotics for functions associated with heat flow on the Sierpinski carpet
Canadian Journal of Mathematics. Journal Canadien de Mathématiques
volume 63
page 153-180
(2011)
Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice
Communications in Mathematical Physics
volume 295
page 29-69
(2010)
Uniqueness for the signature of a path of bounded variation and the reduced path group
Annals of Mathematics. Second Series
volume 171
page 109-167
(2010)
Recent Publications:
A stochastic partial differential equation model for the pricing of mortgage-backed securities
Stochastic Processes and their Applications
(1 January 2018)
CENTRAL LIMIT THEOREMS FOR THE SPECTRA OF CLASSES OF RANDOM FRACTALS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
issue 12
volume 369
page 8967-9013
(December 2017)
Full text available
Spectral asymptotics for V-variable Sierpinski gaskets
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
issue 4
volume 53
page 2162-2213
(November 2017)
Full text available
A forward equation for barrier options under the Brunick & Shreve Markovian projection
QUANTITATIVE FINANCE
issue 6
volume 16
page 827-838
(June 2016)
Full text available
The 3/2 model as a stochastic volatility approximation for a large-basket price-weighted index.
International Journal of Theoretical and Applied Finance
issue 6
volume 18
(September 2015)
Research Interests:
I am a University Lecturer in the Mathematical Institute. I obtained my PhD from the University of Cambridge and held post-doctoral positions at the University of Cambridge and the University of California, San Diego. I previously held academic positions at the Universities of Edinburgh and Bristol before moving to Oxford in 2000.
My research interests are in the area of probability, stochastic processes, mathematical finance and fractals. For further information see my webpage.