Workshop and CAC on Multiplicative Processes

Instructional and Research Workshop on

Multiplicative Processes and Fluid Flows

Thursday 23 - Tuesday 28 August, 2001
Department of Mathematical Sciences, University of Aarhus
Auditorium D3, Building 531

The focus of the workshop was the widespread role of multiplicative structure in various models of flows found in geophysical sciences ranging from turbulent fluids, rainfall, and river networks to internet data flows and cash flows found in financial mathematics.

Tutorial Lectures by Edward C. Waymire

Summary

The lectures included illustrations of modelling hypothesis based on descriptive empirical data and phenomenological scaling arguments leading to rigorous statistical tests and precise mathematical derivations of stochastic multiplicative structure intrinsic to the physical equations of flow. Emphasis wsd given to both model formulation as well as to some general mathematical methods and results for the analysis of such multiplicative structures.

Background in basic probability and stochastic processes was assumed which includes martingales and Markov processes such as Poisson processes, random walk, diffusions, and Galton-Watson branching processes.

List of Speakers

Speaker:	Title:
Rabi N. Bhattacharya, Indiana University:	Multiscale diffusion equations
Alexander Cherny, Moscow State University:	When is a moving average a semimartingale?
Martin Greiner, Max-Planck-Institut für Physik Komplexer Systeme:	From synthetic towards real fully developed turbulence - learning from phenomenology
Vijay Gupta, University of Colorado:	Multiscale hydrologic analyses on self-similar river networks
Francesco Mainardi, University of Bologna:	Fractional diffusion processes: Probability distribution and random walk models
Chris Orum, Oregon State University:	Multiscale diffusion equations
Mina Ossiander, Oregon State University:	Statistical estsimation for multiplicative cascades
Raymond Streater, King's College London:	Correction to fluid dynamics
Enrique Thomann, Oregon State University:	Partial differential equations and multiplicative processes
Brent Troutman, U.S. Geological Survey:	River flow mass exponents with fractal channel networks and rainfall
Giuliano Vitali, University of Bologna:	Flow problems in soil science
Dee Winn, Oregon State University:	Gradient-directed diffusions and river network models

Schedule:



        Thursday 23     Friday 24     Saturday 25     Monday 27   Tuesday 28
----------------------------------------------------------------------------
      
9-10                    Bhattacharya  Waymire         Greiner     Thomann 
      
10-11                   Waymire       Waymire         Greiner     Thomann
      
11-12                   Waymire       Winn            Streater    Orum
      
13-14   Registration      
      
14-15   Waymire         Gupta         Ossiander       Mainardi    Greiner
     
15-16   Waymire         Troutman      Ossiander       Waymire     
      
16-17   Bhattacharya    Troutman      Cherny          Vitali

References

The following list provides some basic references to diverse topics which will be discussed within the broad theme of this workshop.

R.N. Bhattacharya, E. Waymire (1990): Stochastic Processes with Applications, Wiley, NY.
R.N. Bhattacharya, E. Thomann, E. Waymire (2001): The distribution of certain integrals of geometric diffusions.
R.N. Bhattacharya (1999): Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media, Special Invited Paper, Annals of Applied Probability 9(4), 951-1020.
J. Cleve und M. Greiner (2000): The Markovian metamorphosis of a simple turbulent cascade model, Phys. Lett. A 273, 104-108.
H. Eggers, T. Dziekan und M. Greiner: Translationally invariant cumulants in energy cascade models of turbulence, Preprint nlin.CD/0005044, Phys. Lett. A, forthcoming.
V.K. Gupta, E. Waymire (1998): Some mathematical aspects of rainfall, landforms, and floods, in: Stochastic Methods in Hydrology, eds. O.E. Barndorff-Nielsen, V.K. Gupta, V. Perez-Abreu, E. Waymire, Advanced Series on Statistical Science & Applied Probability, vol 7, World Scientific Press, Singapore.
B. Jouault, P. Lipa und M. Greiner (1999): Multiplier phenomenology in random multiplicative cascade processes, Phys. Rev. E 59, 2451-2454.
Y. LeJan and A. Sznitman (1997): Stochastic cascades and 3-dimensional Navier-Stokes equations, Probability Theory and Related Fields 109, 343-366.
M. Ossiander, E. Waymire (2001): Statistical estimation for multiplicative cascades, Annals of Statistics, 28(6).
Z.S. She, E. Waymire (1995): Quantized energy cascade and logPoisson statistics in fully developed turbulence, Phys. Rev. Letters 74(2), 262-265.
B. Troutman, T. Over (2001): River flow mass exponents with fractal channel networks and rainfall, (preprint: troutman@usgs.gov)
E. Waymire, S. Williams (1996): A cascade decompostions theory with applications to Markov and exchangeable cascades, Transactions of the American Mathematical Society 348(2), 585-632.

Participants

Ole E. Barndorff-Nielsen
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmarks
oebn (a) imf.au.dk

Rabi N. Bhattacharya
Dept. of Mathematics Swain East 222
Indiana University
Bloomington IN 47405
USA
bhattach (a) indiana.edu

Alexander Cherny
Moscow State University
Faculty of Mechanics and Mathematics
Dept. of Probability
119899 Moscow
Russia
cherny (a) mech.math.msu.su

Svend Erik Graversen
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
matseg (a) imf.au.dk

Martin Greiner
Max-Planck-Institut für
Physik Komplexer Systeme
Noethnitzer Str. 38
D-01187 Dresden, Germany
greiner (a) mpipks-dresden.mpg.de

Vijay K. Gupta
Department of Civil and Environmental Engineering
Cooperative Institute for Research in Environmental Sciences
University of Colorado
Boulder, USA 80309
gupta (a) terra.colorado.edu

Asger Hobolth
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
asho (a) imf.au.dk

Paulius Jakubenas
Laboratoire de Probabilités
Université Paris VI
4, place de Jussieu
75252 Paris, France
paulius.jakubenas (a) lycos.com

Jens Ledet Jensen
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
jlj (a) imf.au.dk

Salme Kärkkäinen
Department of Statistics
University of Jyväskylä
P.O. Box 35 (MaD)
SF-40351 Jyväskylä, Finland
samk (a) louhi.stat.jyu.fi

Jan-Aake Larsson
Department of Mathematics
Linköping University
SE-581 83 Linköing
Sweden

Francesco Mainardi
Department of Physics
University of Bologna
Via Irnerio 46
I-40126 Bologna, Italy
mainardi (a) bo.infn.it

Elisa Nicolato
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
elisa (a) imf.au.dk

Andrew Olenko
Statistics Department, Mathematics Faculty
Kyiv University
Volodimirska 64
252033 Kyiv, Ukraine
olenk (a) ukma.kiev.ua

Chris Orum
Department of Mathematics
Oregon State University
Corvallis, Oregon 97331
USA
orum (a) math.orst.edu

Mina Ossiander
Department of Mathematics
Oregon State University
Corvallis, Oregon 97331
USA
\ossiand (a) math.orst.edu

Jan Pedersen
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
jan (a) imf.au.dk

Goran Peskir
Department of Mathematical Sciences
University of Aarhus
DK-8000 Aarhus C
Denmark
goran (a) imf.au.dk

Raymond Streater
King's College London
Department of Mathematics
London, WC2R 2LS
UK
ray.streater (a) kcl.ac.uk

Dr. Giuliano Vitali
DISTA
University of Bologna
Via Filippo Re - 6
40126 Bologna, Italy
vitali (a) df.unibo.it

Enrique Thomann
Department of Mathematics
Oregon State University
Corvallis, Oregon 97331
USA
thomann (a) math.orst.edu

Brent Troutman
US Geological Survey
Denver Federal Center
Box 25046, Mail Stop 413, Lake Wood
Co 80225, USA
troutman (a) usgs.gov

Edward C. Waymire
Department of Mathematics
Oregon State University
Corvallis, Oregon 97331
USA
waymire (a) math.orst.edu

Matthias Winkel
Laboratoire de Probabilités et Modèles Aléatoires
Université Pierre et Marie Curie
175 rue du Chevaleret
75013 Paris, France
winkel (a) proba.jussieu.fr

Ronald Dee Winn
Department of Mathematics
Oregon State University
Corvallis, OR 97331
USA
WinnR (a) umpqua.cc.or.us

Geoffrey Yeo
Department of Mathematics and Statistics
University of Western Australia
6009 Nedlands W.A.
Australia
yeo (a) maths.uwa.edu.au

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This document, http://www.maphysto.dk/oldpages/events/MultProc2001/index.html, was last modified May 03, 2004. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.