Analysis, Probability and Stochastic Processes Team
The Analysis, Probability and Stochastic Processes (APSP) interdisciplinary team considers the interface of two areas of mathematics: analysis and probability
The key areas of interest run across the intersection of common research areas of the Mathematical Analysis and Statistics research groups. We are interested in nonlinear PDEs and PDEs with non-local (or fractional) operators and their stochastic representations, stochastic models for for fractional calculus, stochastic homogenisation for PDEs of the first and second order with random coefficients, large deviation theory, diffusion theory and continuous time random walk, fractality and mutifractality, limit theorems for functionals of spatio-temporal random fields and max-stable random fields under weak and strong dependence, spectral theory of random fields, point processes and random fields and extreme values of spatial temporal stochastic processes.
Our activities are focused on promotion and enhancement of collaborations between researchers from the Mathematical Analysis and Statistics research groups through organisation of seminars, workshops, and discussion groups.
We aim to bring together researchers working in different areas of Mathematical Analysis, Probability and Stochastic Processes.
Our researchers are working across disciplines to tackle major challenges facing society, the economy and physical sciences.
The main areas of research within the current group are:
- Nonlinear PDEs and PDEs with non-local (or fractional) operators and their stochastic representations
- Stochastic models for fractional calculus
- Stochastic homogenisation for PDEs of the first and second order with random coefficients
- Scale-bridging and limits of large interacting stochastic systems
- Stochastic and periodic homogenisation, high-contrast homogenisation, high-contrast periodic setting, the high-contrast stochastic problems
- Stochastic representation for evolution by mean curvature flow
- Multi-fractal analysis of stochastic processes and random fields fields
- Pearson diffusions, fractional diffusions, heavy-tailed diffusions, continuous time random walk
- Limit theorems for functionals of spatio-temporal random fields and max-stable random fields under weak and strong dependence
- Spectral theory of random fields
- Limit distributions of the rescaled solutions of linear non-linear partial differential equations with random initial conditions
- Finance and stochastics: fractal activity time models for risky asset with dependence
- Ornstein-Uhlenbeck processes with Levy noise and their superpositions, intermittence
- Point processes and fields with long-range dependence. Fractional Poisson and related random fields, application to insurance
- Extreme values of spatial temporal stochastic processes