A Geometrical Characterization of the Multidimensional Hausdorff and Dale Polytopes with Applications to Exit Time Problems

Please always quote using this URN: urn:nbn:de:0297-zib-7807
  • We present formulae for the corner points of the multidimensional Hausdorff and Dale Polytopes and show how these results can be used to improve linear programming models for computing e.\,g.\ moments of exit distribution of diffusion processes. Specifically, we compute the mean exit time of twodimensional Brownian motion from the unit square and the unit triangle, as well as higher moments of the exit time of time space Brownian motion from a triangle.

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Metadaten
Author:Kurt Helmes, Stefan Röhl
Document Type:ZIB-Report
Tag:Brownian motion on a triangle; linear programming; moment problems; numerical methods for exit time problems; special polytopes
MSC-Classification:44-XX INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10) / 44Axx Integral transforms, operational calculus / 44A60 Moment problems
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J65 Brownian motion [See also 58J65]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C08 Special problems of linear programming (transportation, multi-index, etc.)
Date of first Publication:2004/02/09
Series (Serial Number):ZIB-Report (04-05)
Published in:Part I of the report appeared under the title "A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems" in: Mathematics of Operations Research 33(2):315-326, 2008