A domain-theoretic approach to Brownian motion and general continuous stochastic processes

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• Paul Bilokon
• Friday 21 October 2016, 11:00-12:00
• Computer Science, The Sloman Lounge (UG).

If you have a question about this talk, please contact Paul Taylor.

We introduce a domain-theoretic framework for continuous-time, continuous-state stochastic processes. The laws of stochastic processes are embedded into the space of maximal elements of the normalised probabilistic power domain on the space of continuous interval-valued functions endowed with the relative Scott topology. We use the resulting ω-continuous bounded complete dcpo to define partial stochastic processes and characterise their computability. For a given continuous stochastic process, we show how its domain-theoretic, i.e., finitary, approximations can be constructed, whose least upper bound is the law of the stochastic process. As a main result, we apply our methodology to Brownian motion. We construct a partial Wiener measure and show that the Wiener measure is computable within the domain-theoretic framework. (Joint work with Abbas Edalat.)

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• Computer Science, The Sloman Lounge (UG)
• Theoretical computer science seminar
• computer sience

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