Stochastic Modelling of Small-Scale Perturbation

Small perturbation of stochastic parabolic equations: a power series analysis

A semi-linear second-order stochastic parabolic equation is considered with coefficients, free terms, and initial condition depending on a parameter. It is shown that under some natural conditions the solution can be written as a power series in the parameter. The equations for the coefficients in the power series expansion are derived and the convergence of the power series is studied. An exam...

A Multiple-Scale Stochastic Modelling Primitive

Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling three-dimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements , and by a general lack of user control. We will present a general stochastic modelling primitive that operates on two or more sc...

Cluster-weighted stochastic subgrid-scale modelling

This paper presents the main results of a recent publication (Kwasniok, 2011a). A new approach for data-based stochastic parametrisation of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of ...

A Multiple-Scale Stochastic Modelling Primitive

Instantaneous stochastic perturbation theory

A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.