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IMA 2003 Summer Program
Probability and Partial Differential Equations in Modern Applied Mathematics
July 21-August 1, 2003


Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

Organizers:

Edward C. Waymire (chair)
Mathematics Department
Oregon State University
waymire@math.orst.edu

Jinqiao Duan
Department of Applied Mathematics
Illinois Institute of Technology

duan@iit.edu

This summer program is devoted to the role of probabilistic methods in modern applied mathematics from perspectives of both a tool for analysis and in modeling. Researchers involved in contemporary problems involving dispersion and flow, e.g. fluid flow, cash flow, genetic migration, flow of internet data packets, etc., were selected as speakers and to lead discussion groups. There is a growing recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. In organizing this workshop an explicit effort is being made to bring together researchers with a common interest in the problems, but with diverse mathematical expertise and perspective. In particular, many are researchers who might not ordinarily interact with one another.

The Navier-Stokes equations, Euler equations, Burgers equation etc. arise naturally in the context of the basic physics of fluid motions. As such these equations play a fundamental role in the science and engineering of all varieties of fluid flow, from oceanic circulation to the flow of water beneath the earth's surface. The nonlinearity of the equations makes explicit solutions possible only for the simplest of flows. The development of a more complete understanding of these equations from the laminar to the turbulent regime ranks among the most important outstanding problems of modern mathematical physics.

A probabilistic representation of solutions allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. In addition such approaches can be effective in sorting out multiple scale structure and in the development of Monte Carlo type numerical methods. Among the relevant probability topics are multitype branching random walks, Brownian motion and stochastic calculus, Kolmogorov cascade theory, the vortex method and multiscale methods. In addition to Navier-Stokes equations, other deterministic linear and nonlinear partial differential equations amenable to probabilistic methods of analysis will be of interest in this workshop, e.g. variations on Black-Scholes options equations, contaminant transport, reaction-diffusion, Schrodinger equation, etc.

There is a growing recognition of a role for the inclusion of stochastic terms in the modeling of complex flows. The addition of such terms has led to interesting new mathematical problems at the interface of probability, numerical analysis, and partial differential equaitons. During the last decade, significant progress has been made towards building a comprehensive theory of random dynamical systems, statistical cascades, stochastic flows, stochastic pde's, etc. Some core questions in the modeling, analysis and simulation of complex flows under uncertainty are: exploring appropriate ways to take stochastic effects into account; understanding the impact of randomness on the evolution of complex systems; and designing efficient numerical algorithms to simulate random phenomena.

There is also a need for new ways in which to incorporate the impact of probability, statistics, pde's and numerical analysis in the training of present and future PhD students in the mathematical sciences. The engagement of graduate students is an important feature of this summer program. A poster session will be included in each workshop.

The first workshop will be devoted to the role of probability as an analysis tool as described above. The second workshop will emphasize stochastic methods in connection with modeling of various dispersion and flow scenarios. Thus the combined focus of the two workshops is broadly on probabilistic methods in the modeling and analysis of dispersion and flow, but from two different perspectives.

Workshop 1: July 21-July 25, 2003: Probabilistic Methods in Analysis of PDE's.
Organizers: Edward C. Waymire, Mina E. Ossiander, Enrique A. Thomann, Ronald B. Guenther, Larry Chen (Mathematics, Oregon State University), Rabi N. Bhattacharya (Mathematics, Indiana University)

Workshop 2: July 28-August 1, 2003: Stochastic Models and their Analysis
Organizers:
Jinqiao Duan (Illinois Institute of Technology), Bjorn Schmalfuss (Merseburg), Peter E. Kloeden (Frankfurt), Salah Mohammed (Southern Illinois University), Sri Namachchivaya (UIUC)

WORKSHOP SCHEDULE
Week 1 Monday Tuesday
Week 2 Monday Tuesday
WEEK 1: JULY 21-25, 2003 (Probabilistic Methods in Analysis of PDE's)
MONDAY, JULY 21
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

8:45-9:00 Douglas N. Arnold, Scot Adams, and Organizers Welcome and Introduction
9:00-10:00 Rabi N. Bhattacharya
University of Arizona

Multiscale Diffusions and a Transport Problem in Composite Media

Slides:   html

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Vassili N. Kolokoltsov
Nottingham Trent University

Mathematics of the Feynmann Path Integral Applied to the Schrödinger Equation (Jump Processes Approach)

Preprints:
serbia.pdf      serbia.ps
singular.pdf    singular.ps

12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Zhenqing Chen
University of Washington

Discontinuous Markov Processes and Pseudo-Differential Operators

Reprints/Preprints

Slides:   pdf

3:00-3:30
Discussion
3:30-5:30

POSTER SESSION IMA Tea/Reception
400 Lind Hall

Poster Presenters

TUESDAY, JULY 22
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Mark Freidlin
University of Maryland
Multiparameter Asymptotic Problems for Stochastic Differential Equations and PDE's
10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Charles Newman
Courant Institute
The Brownian Web and Scaling Limits
Reprint/Preprint:  0203184.pdf  0304119.pdf
12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 William G. Faris
University of Arizona

A Gentle Introduction to Cluster Expansions

Slides:   pdf    ps

3:00-3:30
Discussion
WEDNESDAY, JULY 23
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Marco Cannone
Université de Marne-la-Vallée

Smooth and Singular solutions for the Navier-Stokes Equations

Reprints/Preprints:
gravit.pdf
handbook.pdf
modif-NS.pdf
Navier.pdf
sing_reg-NS.pdf

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Enrique Thomann
Oregon State University

Partial Differential Equations and Multiplicative Processes

Slides:
ima.pdf    ima.ps
ima3.pdf    ima3.ps

Paper:
NavierStokesTAMS.pdf
NavierStokesTAMS.ps

12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Sylvie Meleard
MODALX, Université Paris 10-Nanterre
Probabilistic Interpretation and Stochastic Particle Method for Vortex Equations   pdf    ps
3:00-3:30
Discussion
3:30-4:00 Coffee Break Reception Room EE/CS 3-176
4:00-5:00 Robert Krasny
University of Michigan

Particle Simulations of Vortex Sheet Roll-Up in Fluid Dynamics

Slides:   pdf

5:00-5:30
Discussion
THURSDAY, JULY 24
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Siva Athreya
Indian Statistical Institute

Hölder Norm Estimates for Elliptic Operators on Finite and Infinite Dimensional Spaces
abstract.pdf    abstract.ps

Slides:   html

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Priscilla E. Greenwood (Cindy)
Arizona State University

Stochastic Resonance

Slides:   pdf    ps

12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:30 pm 20-minute Talks
2:00-2:30 M. Aslam Chaudhry
King Fahd University of Petroleum & Minerals, Saudi Arabia
Extended Beta Distribution
2:30-3:00 Rolf Moritz Kassman
University of Connecticut

Stochastic Methods for Regularity of Nonlocal Operators of Variable Order

Slides:   pdf    ps

3:00-3:30 Edward C. Waymire
Oregon State University
Remarks on Steady State Limits for NS in Majorizing Spaces: A Probabilistic View
3:30-4:00
Coffee and Posters
Poster Presenters:
Keith Nordstom
University of Colorado at Boulder

Critical Scaling in a Physical Model of Toprical Atmospheric Convection over the Ocean

Preprint:   npg03001.pdf

Michael Tehranchi
University of Texas at Austin

A Characterization of Hedging Portfolios for Interest Rate Contingent Claims

Reprint:    HJMhedge.pdf

Zhihui Yang
University of Maryland, College Park
Exit Problems for System with Perturbations Approximating White Noise   pdf    ps
Jianfeng Zhang
University of Minnesota
The Sharp Rate of Numerical Methods for Degenerate ODEs    pdf    ps
4:00-5:30
Posters and 20-minute Talks
4:00-4:30 Marco Romito
Università di Firenze
A Probabilistic Representation for the Vorticity of a 3D Viscous Fluid and for General Systems of Parabolic Equations
4:30-5:00 Peter Friz
Courant Institute

Rough Paths and Approximation

Slides:   pdf

5:00-5:30 Chris Orum
Oregon State University
On the Explosion Problem and KPP
FRIDAY, JULY 25
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Boris L. Rozovskii
University of Southern California

Stochastic Navier-Stokes Equations for Turbulent Flows: Propagation of Chaos and Moments Problem

Preprints:
NSEQANNALSa.pdf
NSEQANNALSa.ps
NSESIAM7IMA.pdf
NSESIAM7IMA.ps

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Wojbor A. Woyczinski
Case Western Reserve University
Nonlinear Partial Differential Equations Driven by Levy Diffusions and Related Statistical Issues
12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Martin Greiner
Siemens AG, CT IC 4

Data-Driven Stochastic Processes in Fully Developed Turbulence

Reprints: greiner_EPL61_2003_756.pdf
greiner_PhysicaA325_2003_577.pdf
greiner_PLA266_2000_276.pdf
greiner_PhysicaD136_2000_125.pdf
greiner_PhysicaA247_1997_41.pdf
greiner_PLA273_2000_104.pdf
greiner_PLA281_2001_249.pdf
greiner_PRE51_1995_1948.pdf
greiner_PRE58_1998_554.pdf
greiner_PRE59_1999_2451.pdf
greiner_PRL80_1998_5333.pdf

3:00-3:30
Discussion
3:30-4:00 Coffee Break Reception Room EE/CS 3-176
4:00-5:00 Cecile Penland
NOAA-CIRES/Climate Diagnostics Center

Do We Really Need to Describe Every Single Leaf in a Climate Model?: Applications of the Central Limit Theorem

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Page.7a.pdf Page.7a.ps
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Page.12.pdf Page.12.ps
references.pdf references.doc
5:00-5:30
Discussion
WEEK 2: JULY 28-AUGUST 1, 2003 (Stochastic Models and their Analysis)
MONDAY, JULY 28
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Salah-Eldin A. Mohammed
Southern Illinois University, Carbondale
The Stable Manifold Theorem for Semi-Linear Stochastic Partial Differential Equations
10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Kening Lu
Michigan State University
Invariant Manifolds for Stochastic PDE's
12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Björn Schmalfuss
University of Applied Sciences Merseburg

Stochastic Partial Differential Equations and Random Dynamical Systems

Slides:   html

3:00-3:30
Discussion
3:30-4:00 Coffee Break Reception Room EE/CS 3-176
4:00-5:00 Hao Wang
University of Oregon

A Class of Conditional Independent Branching Particle Systems and Their Interacting Limit Superprocesses

Slides:
html    pdf    ps    ppt

Papers:
DLW_rev.pdf
SinDeg.pdf

5:00-5:30
Discussion
TUESDAY, JULY 29
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Rene Carmona
Princeton University

Malliavin Calculus for Stochastic Partial Differential Equations

Slides:   pdf

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Victor W. Goodman
Indiana University

Interest Rate Explosions in HJM Bond Models

Slides:   pdf    ps

12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-2:30 Jinqiao Duan
Illinois Institute of Technology
Ergodicity, Fluctuations and Stabilization in Fluid Flows
2:30-3:00
Keith Nordstrom
University of Colorado at Boulder
Critical Scaling in a Physical Model of Convective Rainfall
WEDNESDAY, JULY 30
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Yves Le Jan
Universite Paris Sud XI

Flows, Coalescence, Noise and Glue

Papers:   Bmatrix.pdf Bmatrix.ps
artsticky.pdf
artsticky.ps
coalflow.pdf
coalflow.ps

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Erhan Cinlar
Princeton University
Stochastic Flows with Jumps
12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Michael Scheutzow
Technische Universität Berlin
On the Dispersion of Sets Under the Action of an Isotropic Brownian Flow
3:00-3:30
Discussion
THURSDAY, JULY 31
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Hassan Allouba
Kent State University

From Brownian-Time Processes to Linearized Kuramoto-Sivashinsky PDE

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Ian M. Davies
University of Swansea

Stochastic Heat and Burgers Equations and their Singularities

Slides:   pdf

12:00-12:30
Discussion
12:30-2:00
Lunch Break
2:00-3:00 Michael Cranston
University of Rochester
Some Recent Results on the Parabolic Anderson Model
3:00-3:30
Discussion
3:30-4:00 Coffee Break Reception Room EE/CS 3-176
4:00-5:00 Dirk Blömker
University of Warwick

Structure of Invariant Measures Near Bifurcations

Preprints:   cubicsub.pdf     cubicsub.ps    quadratic03.pdf    quadratic03.ps

5:00-5:30
Discussion
FRIDAY, AUGUST 1
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:45-9:00 Coffee Reception Room EE/CS 3-176
9:00-10:00 Mukul Majumdar
Cornell University

Random Dynamical Systems with Monotone Laws of Motion: Examples from Economics

Paper:   pdf

10:00-10:30
Discussion
10:30-11:00 Coffee Break Reception Room EE/CS 3-176
11:00-12:00 Krishna B. Athreya
Cornell University and Iowa State University
Markov Chains Generated by Iteration of iid Maps on R+
12:00-12:30
Discussion
 
Concluding Remarks by Organizers
 
End of Conference

POSTER PRESENTERS
Michele L. Baldini
New York University
The invariant measure of a infinite dimensional diffusion: how can we compute it?
Siwei Jia
Oregon State University
A Note on the Economic Management of Inventory or Resource under Stochastic Prices
Kyounghee Kim
Indiana University, Bloomington
Moment Generating Function of the Reciprocal of Integral of Geometric Brownian Motion
Panki Kim
University of Washington

Abstract:   fcabstract.pdf    fcabstract.ps

Preprint:    fatoucensored.pdf    fatoucensored.ps

 Vassili N. Kolokoltsov
Nottingham Trent University

Measure-valued Limits of Interacting Particle Systems with k-nary Interaction

Preprints:
fel.pdf    fel.ps
p2.pdf    p2.ps
p4nn.pdf    p4nn.ps
super.pdf    super.ps

Keith Nordstom
University of Colorado at Boulder

Critical Scaling in a Physical Model of Toprical Atmospheric Convection over the Ocean

Preprint:   npg03001.pdf

Jorge Mario Ramirez
Oregon State University
A Multiplicative Cascade Monte Carlo Solution to Linear Diffussion in Fourier Domain
abstract.pdf   abstract.ps
Marco Romito
Università di Firenze
A Probabilistic Representation for the Vorticity of a 3D Viscous Fluid and for General Systems of Parabolic Equations
Michael Tehranchi
University of Texas at Austin

A Characterization of Hedging Portfolios for Interest Rate Contingent Claims

Reprint:    HJMhedge.pdf

Zhihui Yang
University of Maryland, College Park
Exit Problems for System with Perturbations Approximating White Noise   pdf    ps
Jianfeng Zhang
University of Minnesota
The Sharp Rate of Numerical Methods for Degenerate ODEs    pdf    ps
Week 1 Monday Tuesday
Week 2 Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS

As of 8/6/2003
Name Department Affiliation
Scot Adams IMA University of Minnesota
Hassan Allouba Mathematical Sciences Kent State University
Anna Amirdjanova Statistics University of Michigan
Douglas N. Arnold IMA University of Minnesota
Krishna Athreya   Cornell University
Siva Athreya   Indian Statistical Institute, New Delhi
Paul Atzberger Mathematics (Stochastic Processes) New York University - Courant Institute
Gerard Awanou Mathematics University of Georgia
Michele Baldini Physics New York University
Rabi Bhattacharya Mathematics Indiana University
Dirk Bloemker Mathematics Research Center University of Warwick
Maury Bramson   University of Minnesota
Susanne C. Brenner   University of South Carolina
Maria Carme Calderer Mathematics University of Minnesota
Marco Cannone Laboratoire d'Analyse et de Mathématiques Appliqué Université de Marne-la-Vallée
Rene Carmona   Princeton University
Fernando Carreon Mathematics University of Texas - Austin
Panagiotis Chatzipantelidis Mathematics Texas A&M University
M. Aslam Chaudhry Mathematical Sciences King Fahd University of Petroleum & Minerals
Larry Chen Mathematics Oregon State University
Long Chen Mathematics Pennsylvania State University
Zhenqing Chen   University of Washington
Lan Cheng Mathematics University of Pittsburgh
Erhan Cinlar Operations Research & Financial Eng Princeton University
Michael Cranston Mathematics University of Rochester
Ian M. Davies Mathematics University of Wales Swansea
Hongjie Dong Mathematics University of Minnesota
Jinqiao Duan   Illinois Institute of Technology
Valdo Durrleman   Bendheim Center for Finance
Maria Emelianenko Mathematics Pennsylvania State University
William Faris Mathematics University of Arizona
Mark Freidlin Mathematics University of Maryland, College Park
Peter Friz   Courant Institute
Victor Goodman Mathematics Indiana University
Priscilla E. Greenwood Mathematics Arizona State University
Martin Greiner   Max Planck Institute for the Physics of Complex Sys
Ernesto Gutierrez-Miravete Engineering and Science Rensselaer Polytechnic Institute
Naresh Jain Mathematics University of Minnesota
Siwei Jia Statistics Oregon State University
Yu-Juan Jien Mathematics Purdue University
Yoon Mo Jung Mathematics University of Minnesota
G Kallianpur Statistics University of North Carolina
Rolf Moritz Kassmann Mathematics University of Connecticut
Markus Keel   University of Minnesota
Djivede Kelome Mathematics and Statistics University of Massachusetts
Eun Heui Kim   California State University - Long Beach
Kyounghee Kim Mathematics Indiana University
Panki Kim Mathematics University of Washington
Vassili N. Kolokoltsov Mathematics Nottingham Trent University
Yuriy Kolomiyets Mathematics Kent State University
Robert Krasny Mathematics University of Michigan
Yves LeJan Département de Mathématiques University Paris Sud
Seung Lee Mathematics Ohio State University
Guang-Tsai Lei   Mayo Clinic
Runchang Lin Mathematics Wayne State University
Yuping Liu Mathematics Purdue University
Kening Lu Mathematics Michigan State University
Mukul Majumdar Economics Cornell University
Rogemar Mamon Statistics and Actuarial Science University of Waterloo
Sylvie Meleard UFR Segmi Université Paris X
Oana Mocioalca Mathematics Purdue University
Salah Mohammed Mathematics Southern Illinois University
Charles M. Newman   New York University
Mahdi Nezafat Electrical and Computer Engineering University of Minnesota
Keith Nordstrom C4-CIRES University of Colorado at Boulder
Chris Orum   Oregon State University
Mina Ossiander Mathematics Oregon State University
Chetan Pahlajani Mathematics University of Illinois - Urbana-Champaign
Veena Paliwal Mathematics Southern Illinois University
Jun Hyun Park   University of Illinois - Urbana-Champaign
Cecile Penland NOAA-CIRES University of Colorado
Lea Popovic Statistics University of California - Berkeley
Jorge M. Ramirez Mathematics Oregon State University
Vivek Ranjan Mathematics Indiana University
Marco Romito Dipartimento di Matematica Universita' di Firenze
Boris Rozovskii   University of California - Los Angeles
Fadil Santosa IMA University of Minnesota
David Saunders Mathematics University of Pittsburgh
Michael Scheutzow Fakultät II, Institut für Mathematik Technische Universität Berlin
Bjoern Schmalfuss Science University of Merseburg
Rongfeng Sun Courant Institute New York University
Li-Yeng Sung   University of South Carolina
Michael Tehranchi Mathematics University of Texas - Austin
Enrique Thomann Mathematics Oregon State University
Ilya Timofeyev Mathematics University of Houston
Daniell Toth Mathematics Juniata College
Hao Wang   University of Oregon
Jing Wang Institute for Mathematics and its Application University of Minnesota
Li Wang Probability and Statistics Michigan State University
Lixin Wang Operations Research and Financial Engineering Princeton University
Ed Waymire Mathematics Oregon State University
Hans Weinberger Mathematics University of Minnesota
Andrew Westmeyer Mathematics University of Wyoming
Wojbor A. Woyczynski Statistics Case Western Reserve University
Jian Yang Mathematics University of Illinois - Urbana-Champaign
Zhihui Yang Mathematics University of Maryland, College Park
Aaron Nung kwan Yip Mathematics Purdue University
Toshio Yoshikawa University of Minnesota Institute for Mathematics and its Applications
Jianfeng Zhang Mathematics University of Minnesota
Tao Zhang Mathematics Purdue University
Yongcheng Zhou Mathematics Michigan State University
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