Stochastic models

Actin polymerization in vivo is regulated spatially and temporally by a web of signaling proteins. We developed detailed physico-chemical, stochastic models of lamellipodia and filopodia, which are projected by eukaryotic cells during cell migration, and contain dynamically remodeling actin meshes and bundles. In particular, we investigated how molecular motors regulate growth dynamics of elongated organelles of living cells.

It is often desirable to derive an effective stochastic model for the physical process from observational and/or numerical data. Various techniques exist for performing estimation of drift and diffusion in stochastic differential equations from discrete datasets. In this talk we discuss the question of sub-sampling of the data when it is desirable to approximate statistical features of a smooth trajectory by a stochastic differential equation. In this case estimation of stochastic differential equations would yield incorrect results if the dataset is too dense in time.

This lecture discusses the theoretical framework, observational evidence, and related developments in stochastic modeling of weather and climate extremes.

Geostrophic eddies control the meridional mixing of heat, carbon, and other climatically important tracers in the Southern Ocean. We will report the first direct estimates of eddy mixing across the Southern Ocean from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean. The estimates are based on the dispersion of an anthropogenic tracer and floats over a period of two years. We find that mixing is weak in the upper 2 km and enhanced at depth.

In the tropics, storms and convection occur intermittently and have a major impact on weather and climate, yet they are sub grid-scale processes for General Circulation Models (GCMs). This talk presents two prototype stochastic models for representing these effects in GCMs. The first model is aimed at precipitation statistics that resemble critical phenomena from statistical physics, including power-law distributions and long-range correlations.

In this lecture it will be shown how basic concepts of
Probability Theory, such as distribution, independence,
(conditional) expectation, can be extended to the case of
random sets and random (lower semi-continuous)
functions. Then, some convergence results for sequences of
random sets and random functions, already known for
sequences or real-valued random variables, will be presented.
It will be also shown how these results give rise to
various applications to the convergence or approximation of

Classical stochastic models for chemical reaction networks are
given by continuous time Markov chains. Methods for characterizing these
models will be reviewed focusing primarily on obtaining the models as
solutions of stochastic equations. The relationship between these equations
and standard simulation methods will be described. The primary focus of the
talk will be on employing stochastic analytic methods for these equations to
understand the multiscale nature of complex networks and to exploit the