I am a lecturer in the School of Mathematics
with research interests
in theoretical, computational and applied aspects of
stochastic analysis and partial differential equations.
School of Mathematics, University of Edinburgh
Room 4611, JCMB, King's Buildings
Tel. 0131 651 9091
Students interested in working on a PhD project (to start in September 2018)
in the areas of:
should contact me with informal enquires: email@example.com.
- stochastic partial differential equations,
- non-linear partial differential equations,
- stochastic control theory,
- computational methods and applications of the above (in engineering, biology,
See the School PhD applications website for more details regarding applications.
Funding is available either through the School or via the Maxwell Institute Graduate School in Analysis and Applications (MIGSAA).
Here are some events I am (or was) helping to organize.
- With I. Gyöngy,
Itô Formula for Processes Taking Values in Intersection of Finitely Many Banach Spaces,
Stoch. PDE: Anal. Comp., 5(3), 428-455, 2017.
- With E. Emmrich,
Nonlinear stochastic evolution equations of second order with damping,
Stoch. PDE: Anal. Comp., 5(1), 81-112, 2017.
- With I. Gyöngy and S. Sabanis,
Convergence of tamed Euler schemes for a class of stochastic evolution equations,
Stoch. PDE: Anal. Comp., 4(2), 225-245, 2016.
- With E. Emmrich and A. Wroblewska-Kaminska, Equations of second order in time with quasilinear damping:
existence in Orlicz spaces via convergence of a full discretisation,
Math. Methods Appl. Sci., 39(10), 2449-2460, 2016. (preprint version).
- With E. Emmrich and M. Thalhammer, On a full discretisation for nonlinear second-order evolution equations with monotone damping: construction, convergence, and error estimates,
Found. Comput. Math. 2015
- With E. Emmrich, Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization, J. Diff. Eq., 255 (2013), no. 10, 3719-3746
- With E. Emmrich, Full discretization of the porous medium/fast diffusion equation based on its very weak formulation , Commun. Math. Sci., 10 (2012), no. 4, 1055-1080
- Error estimates for finite difference approximations of American put option price, CMAM, 12 (2012), no. 1, 108-120
- With E. Emmrich, Full discretization of second-order nonlinear evolution equations: strong convergence and applications to elasticity theory, CMAM, 11 (2011), no. 4, 441-459
- With I. Gyöngy, On Finite-Difference Approximations for Normalized Bellman Equations, Appl. Math. Optim., 60 (2009), no. 3, 297-339
- With I. Gyöngy, On Randomized Stopping, Bernoulli, 14 (2008), no. 2, 352–361
Numerical Computation Output Examples
- The solution of a stochastic Ginzburg-Landau equation in one spatial dimension using a newly developed Tamed Euler scheme (see related article)
The solution to vibrating membrane equation with nonlinear damping (see related article)
- The payoff of an American put option, obtained using finite difference method, with the optimal exercise boundary indicated and a sample path of the price process (see related article)
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