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Reading Group on Stochastic Differential Equations

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We are interested in the modelling of continuous-time continuous state stochastic processes from uncertain observations. Such processes, also known as diffusion processes, describe dynamical systems andarise in a wide range of applications, e.g. numerical weather prediction, finance and genetic networks. Often, we may assume that the dynamical models are formulated by systems of differential equations.

The reading group will first study the theory of diffusion processes and their mathematical description by stochastic differential equations (SDEs). We are interested in the basics of Ito stochastic calculus, solvable SDEs, stochastic Taylor expansions and time discrete approximation of SDEs.

Next, recent advances in the field will be discussed. To mention one example, when following a Bayesian approach, we may incorporate a priori knowledge about the dynamics by providing probability distributions on the unknown functions, which correspond for example to driving forces and appear as coefficients or parameters in the differential equations. Hence, such functions become stochastic processes in a probabilistic Bayesian framework.

The main reference material for the reading group can be found in Numerical Solutions to Stochastic Differential Equations by Kloeden and Platen (1999, second edition). The reading groups will take place on Thursdays from 11:00 until 12:30, usually in room 6.12 or 6.12a, Malet Place Engineering Building, Department of Computer Science, University College London.

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