Imperial College London
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ProfessorAbbasEdalat

Faculty of Engineering, Department of Computing

Professor in Computer Science & Maths
 
 
 
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Contact

 

+44 (0)20 7594 8245a.edalat Website

 
 
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Location

 

420Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Bilokon:2017:10.1016/j.tcs.2017.07.016,
author = {Bilokon, P and Edalat, A},
doi = {10.1016/j.tcs.2017.07.016},
journal = {Theoretical Computer Science},
pages = {10--26},
title = {A domain-theoretic approach to Brownian motion and general continuous stochastic processes},
url = {http://dx.doi.org/10.1016/j.tcs.2017.07.016},
volume = {691},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We  introduce  a  domain-theoretic  framework  for  continuous-time,  continuous-statestochastic processes.  The laws of stochastic processes are embedded into the spaceof maximal elements of the normalised probabilistic power domain on the space ofcontinuous interval-valued functions endowed with the relative Scott topology. We usethe resultingω-continuous bounded complete dcpo to obtain partially defined stochas-tic processes and characterise their computability.  For a given continuous stochasticprocess, we show how its domain-theoretic, i.e., finitary, approximations can be con-structed,  whose  least  upper  bound  is  the  law  of  the  stochastic  process.   As  a  mainresult, we apply our methodology to Brownian motion.  We construct a partially de-fined  Wiener  measure  and  show  that  the  Wiener  measure  is  computable  within  thedomain-theoretic framework.
AU  - Bilokon,P
AU  - Edalat,A
DO  - 10.1016/j.tcs.2017.07.016
EP  - 26
PY  - 2017///
SN  - 0304-3975
SP  - 10
TI  - A domain-theoretic approach to Brownian motion and general continuous stochastic processes
T2  - Theoretical Computer Science
UR  - http://dx.doi.org/10.1016/j.tcs.2017.07.016
UR  - http://hdl.handle.net/10044/1/48549
VL  - 691
ER  -
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