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Mathematical Homepage of Jochen Voss

By Jochen Voss, last updated 2012-11-15

This page gives a short summary of my mathematical interests.

Contents

Conditional Path Sampling of SDEs

With Andrew Stuart and Martin Hairer I am exploring how infinite dimensional Langevin sampling can be used to sample from conditioned distributions of solutions of stochastic differential equations. Our method is based on constructing a partial stochastic differential equation which has the conditioned target density as its stationary distribution.

Example: the following picture shows a path from the solution of a stochastic differential equation on the time interval [0,100], conditioned on having the value -1 at time 0 and having the value +1 at time 100. The drift has -1 and +1 as stable equilibrium points and 0 as an unstable equilibrium point.

[doublewell]

This method yields a new algorithm for the (non-linear) Kalman filter/smoother. One can view the pair of signal and observation as the solution of a two-dimensional stochastic differential equation. Our method can then be used to study the distribution of the signal conditioned on a given observation.

Diffusion Processes

Together with my brother Andreas Voss I work on a parameter estimation problem for diffusion processes which arises in psychology when modelling speeded binary decision processes.

My Diplomarbeit (approximately equivalent to an MSc thesis) deals with a topic related to diffusion processes: There I consider the question how fast one can distinguish between two different given diffusions, when observing a single path over long intervals of time.

Large Deviations

In my PhD thesis I prove a large deviation result about the behaviour of diffusions under a strong drift.

Simulations and Numerical Analysis

Miscellaneous

Copyright © 2012, Jochen Voss. All content on this website (including text, pictures, and any other original works), unless otherwise noted, is licensed under a Creative Commons Attribution-Share Alike 3.0 License.