# Session:Stochastic Integration<br>Organizer:

Saturday, August 6, 2005 - 8:45am - 10:30am

EE/CS 3-180

Terence Lyons (University of Oxford)

**Anticipating stochastic calculus via good rough path sequences**

Peter Friz (New York University)

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the stochastic process, the unique solution of the above SDE understoof in the rough path sense is actually a Stratonovich solution. This condition is satisfied by Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/4.**Applications of rough paths to speech recognition**

Anastasia Papavasiliou (Princeton University)

It is a well known fact that when someone speaks, the signal reaching the human ear is the original signal produced by the speaker and several delays. We think of this as a multidimensional rough path. Using tools coming from the theory of rough paths, I will construct much simpler rough paths (piecewise linear) approximating the one containing the speech signal and its delays, which still cause a similar response. Thus, the constructed rough paths contain all the information relevant to the response. If we think of the meaning of the speech signal as the response, the constructed rough paths will contain the meaning in a much more robust way than the signal itself, and thus can be used to construct a likelihood function for each word.**Stochastic integrals for processes with long-time memory**

Zhongmin Qian (University of Oxford)

Stochastic processes with long-time memory have been used extensively in modelling random phenomena. In this talk I will discuss the theory of rough paths and its application to a class of stochastic dynamical systems driven by such long-time memory.