Many real-life situations seem to demonstrate a degree of randomness – from molecules bouncing off each other in the air around us to fluctuations in the stock market.
This randomness, or stochasticity, is an important part of realistic mathematical and statistical models but is difficult to analyse.
Some of the more exotic functions that occur in mathematics, such as those that are not differentiable anywhere, can play an important role in models of randomness.
Stochastic analysis has therefore become an increasingly important part of the mathematical sciences, allowing understanding of real-world situations where random behaviour is crucial.
The Stochastic Analysis research group works on the theoretical and methodological problems of various types of stochastic processes in space and time.
Group members have also formed a widely distributed network of national and international collaborators, in academia and the business world. If you're interested in collaborating with us or wish to enquire about postgraduate or postdoctoral research positions then please contact one of the group members listed below.
Our research interests
Stochastic Differential Equations
- Existence-and-uniqueness theorems
- Stochastic stability, stabilisation and control
- Stochastic asymptotic analysis
- Stochastic population dynamics
- Numerical solutions of stochastic differential equations
- Numerical methods for stochastic stability
- Applications to mathematical finance
- Dimension reduction for multivariate time series
- Non-linear models and their applications in finance
- Financial econometrics
- Functional time series analysis
- Extreme statistics and risk management
- Empirical processes and related limit theorems
- Random spatial graphs
- Random walks
- Image segmentation and measurement, especially cell microscope images
- Colour image analysis
- Applications combining pattern recognition and image analysis
- Prediction of time state of images of evolving textures
- Morphological image processing
- Image quality measures