# How to build a stochastic bridge

#### How to build a stochastic bridge

- Event time: 11:30am
- Event date: 24th September 2014
- Speaker: Dr Juraj Szavits Nossan (School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Stochastic bridge is a process that is assumed to have known (fixed) values at times 0 and T. I will begin by constructing perhaps the simplest of all bridges called Wiener bridge, which uses the Wiener process for the conditioning. Later, I will show how to systematically build a bridge starting from any stochastic differential equation. Stochastic bridges are of particular interest when the fixed value at T is an atypical event, in which case the problem is to find a typical trajectory leading to such a rare event. Finding such trajectories in general and for various conditionings is beginning to attract a lot of interest in nonequilibrium statistical physics. Particularly surprising case is that of Ornstein-Uhlenbeck bridge condition on a rare event, in which the conditioned process behaves just as the original process until the very end, when it suddenly jumps to the prescribed fixed value.

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