The following speakers have confirmed to present mini-courses:
- Evelyn Buckwar (Linz, Austria):
Stability theory for numerical methods for stochastic
This course is concerned with the following topics: Linear stability theory, mean-square stability, almost sure stability, nonlinear stability results. Slides part 1, slides part 2, slides part 3.
- Desmond Higham (Strathclyde, United Kingdom):
Stochastic simulation in chemistry and finance
(1) Gillespie's algorithm and its relation to SDEs (slides); (2) Tau-leaping and multilevel approximations to Gillespie (slides); (3) Monte-Carlo/SDEs in mathematical finance (slides). Handout.
- Gabriel Lord (Edinburgh, United Kingdom):
Stochastic PDEs and their numerical approximation
The lectures will introduce space-time noise and consider Q-Wiener processes and the Ito stochastic integral for this case. We will examine mild solutions of a semilinear stochastic PDE, introduce numerical methods, discretising in both space and in time, and examine convergence. Throughout we will illustrate these concepts with simple numerical codes. Slides.
- Andreas Rößler (Lübeck, Germany):
Introduction to weak and strong approximation methods for
stochastic differential equations
(1) Brief introduction to SDEs and Ito's formula, stochastic Taylor expansion, weak and strong approximation of solutions, Taylor schemes (slides); (2) introduction to stochastic Runge-Kutta methods, rooted tree theory, weak and strong approximation schemes, order conditions, implementation issues (slides); (3) the idea of multi-level Monte Carlo simulation with applications to mathematical finance (slides).
- Peter Friz (TU and WIAS Berlin, Germany): Rough path analysis
We shall explain the basic ideas of rough path analysis and indicate their significance for weak and strong approximation schemes, both for SDEs and SPDEs.
- Annika Lang (ETH Zürich, Switzerland): Simulating the driving noise of a
stochastic partial differential equation
It is well-known that the simulation of the solution of a stochastic partial differential equation requires discretization in space and time. In this talk we observe that the implementation of these approximations might still cause problems since the simulation of the driving noise requires the generation of infinitely many random numbers. We introduce approximations of the driving noise and show that theses do not dominate the overall convergence of the discretization scheme if the parameters are chosen appropriately.
- John Schoenmakers (WIAS Berlin, Germany): Simulation of conditional diffusions via
forward-reverse stochastic representations
In this talk we present stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers, Spokoiny (2004) in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, hence they do not suffer from the curse of dimensionality. This is joint work with Christian Bayer. (Slides)