Table Of ContentProgress in Systems and Control Theory
Volume 23
Series Editor
Christopher I. Byrnes, Washington University
1. Csiszar
Gy. Michaletzky
Stochastic Differential
and Difference Equations
Springer Science+Business Media, LLC
Imre Csiszru- Gyorgy Michaletzky
Mathematical Institute of the Eotvos Lorănd University
Hungarian Academy of Sciences Department of Probability Theory
Realtanoda u. 13-15 and Statistics
Budapest 1053 Muzeum krt. 6-8
Hungary Budapest 1088, Hungary
Library of Congress Cataloging-in-Publication Data
Stochastic differential and difference equations / Imre Csiszru-and
Gyorgy Michaletzky, editors.
p. cm. -- (Progress in systems and control theory; v. 23)
Papers from the Conference on Stochastic Differential and
Difference Equations held Aug. 21-24, 1996, in Gyor, Hungary.
Includes bibliographical references.
ISBN 978-1-4612-7365-3 ISBN 978-1-4612-1980-4 (eBook)
DOI 10.1007/978-1-4612-1980-4
hc : alk. paper)
1. Stochastic differential equations--Congresses. 2. Stochastic
difference equations--Congresses. 1. Csiszru-, Imre, 1938-
II. Michaletzky, Gyorgy, 1950- . III. Conference on Stochastic
Differential and Difference Equations (1996 : Gyor, Hungary)
IV. Series.
QA274.23.S8 1997
519.2--dc21 97-20913
CIP
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Table of Contents
Table of Contents ..................................................... v
Preface ............................................................... ix
Gyar. The Conference Venue ......................................... xi
List of Participants .................................................. xiii
Periodically Correlated Solutions to a Class of Stochastic
Difference Equations
Georgi N. Boshnakov ................................................... 1
On Nonlinear SDE'S whose Densities Evolve in a
Finite-Dimensional Family
Damiano Brigo ....................................................... 11
Composition of Skeletons and Support Theorems
Maria Emilia Caballero, Begofia Fernandez, and David Nualart ....... 21
Invariant Measure for a Wave Equation on a Riemannian Manifold
A.B. Cruzeiro and Z. Haba ........................................... 35
Ergodic Distributed Control for Parameter Dependent Stochastic
Semilinear Systems
T.E. Duncan, B. Maslowski, and B. Pasik-Duncan ................... 43
Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation
M asatoshi Fukushima ................................................ 59
Rate of Convergence of Moments of Spall's SPSA Method
Laszl6 Gerencser .................................................... 67
General Setting for Stochastic Processes Associated with Quantum Fields
Sergio Albeverio, Roman Gielerak, and Francesco Russo .............. 77
On a Class of Semilinear Stochastic Partial Differential Equations
Istvan Gyongy ....................................................... 91
Parallel Numerical Solution of a Class of
Volterra Integra-Differential Equations
Gerd Heber and Christoph Lindemann ............................... 123
vi Table of Contents
On the Laws of the Oseledets Spaces of Linear Stochastic
Differential Equations
Peter Imkeller ...................................................... 133
On Stationarity of Additive Bilinear State-space Representation of
Time Series
Marton Ispany ..................................................... 143
On Convergence of Approximations of Ito-Volterra Equations
Alexander Kolodii ................................................... 157
Non-isotropic Ornstein-Uhlenbeck Process and
White Noise Analysis
Izumi Kubo ........................................................ 167
Stochastic Processes with Independent Increments on a Lie Group
and their Selfsimilar Properties
Hiroshi Kunita ...................................................... 183
Optimal Damping of Forced Oscillations Discrete-time Systems
by Output Feedback
Anders Lindquist and Vladimir A. Yakubovich ...................... 203
Forecast of Levy's Brownian Motion as the
Observation Domain Undergoes Deformation
Laszlo Markus ...................................................... 233
A Maximal Inequality for the Skorohod Integral
Elisa Alos and David Nualart ....................................... 241
On the Kinematics of Stochastic Mechanics
Michele Pavon ...................................................... 253
Stochastic Equations in Formal Mappings
Igor Spectorsky ..................................................... 267
On Fisher's Information Matrix of an ARMA Process
Andre Klein and Peter Spreij ....................................... 273
Statistical Analysis of Nonlinear and NonGaussian Time Series
T. Subba Rao ...................................................... 285
Bilinear Stochastic Systems with Long Range Dependence
in Continuous Time
E. Igloi and Gy. Terdik ............................................ 299
Table of Contents vii
On Support Theorems for Stochastic Nonlinear Partial
Differential Equations
K rystyna Twardowska .............................................. 309
Excitation and Performance in Continuous-time Stochastic
Adaptive LQ-control
Zs. Vago .......................................................... 319
Invariant Measures for Diffusion Processes in Conuclear Spaces
Jie Xiong ......................................................... 329
Degree Theory on Wiener Space and an
Application to a Class of SPDEs
A. Siileyman Ustiinel and Moshe Zakai ............................. 339
On the Interacting Measure-Valued Branching Processes
X ueLei Zhao ......................................................... 345
Preface
The Conference on Stochastic Differential and Difference Equations
held at Gyor, Hungary, August 21-24,1996 was organized jointly by Eotvos
Lonind University, Budapest and Kossuth Lajos University, Debrecen, with
the sponsorship of the Hungarian Regional, the International Executive and
the European Regional Committees of the Bernoulli Society as a satellite
event to the 4th World Congress of the Bernoulli Society, August 26-31,
1996, Vienna, Austria.
It is noteworthy that the meeting had a strong international flavour
with 76 participants from 21 countries, including 6 each from Japan and
the USA. The core of the conference consisted of the 14 invited lectures,
delivered by distinguished experts in their research fields. The majority of
contemporary research areas have been covered in these lectures.
The list of the invited speakers included T. Duncan, M. Fukushima, T.
Funaki, 1. Gyongy, R. Khasminskii, 1. Kubo, H. Kunita, A. Lindquist, D.
Nualart, R. Ober, M. Pavon, G. Picci, T. SubbaRao, M. Zakai.
Invited lectures were presented in plenary sessions, while the con
tributed papers were presented in two parallel sessions. The first session
was devoted to various problems of stochastic partial differential equations
(SPDE) and related random fields. The second session covered discrete
and continuous time parameter ARMA processes and stochastic differen
tial equations in general.
The Szechenyi Istvan College in Gyor provided the venue of the event,
seemingly the satisfaction of the participants.
The Welcome party and the Gala Dinner, with its fabulous cuisine and
Hungarian wines, provided the guests with gracious and pleasing enter
tainments. These occasions proved to be golden opportunities to meet old
friends and make new ones from all over the world.
Budapest, Febr. 25, 1997
Csiszar Imre Michaletzky Gyorgy Markus Laszl6
chairman chairman secretary
Gyor. The Conference Venue
Gyar is called town of the waters, because it lies at the confluence of
the Danube, Raba, Rabca and Marcall Rivers. It has made history over
many centuries. In the 5th century B.C. Gyar was inhabited by Celtic and
Illyrian tribes. The Romans took over from them but kept the Illyrian name
of Arrabona, which means, dwellings by the River Rab". Arrabona -thanks
to its strategic location - soon became an important town, aqd fortress of
Pannonia Province. After the fall of the Roman Empire the Avars ruled
the town and they fortified the Roman "Castrum" by ring-shaped mounds.
This is how the settling Hungarians found the castle, and from the ring
(ring - gyuru in Hungarian) they gave it its name. The Hungarians also
recognised the strategic importance of the place. Already during the reign
of the first king Stephen 1st, it had become an episcopal seat, turning very
soon into a cathedral town. In 1271 King Stephen 5th elevated Gyar to
the rank of free royal town and gave the right to tax traffic in transit.
During the Turkish invasion strategic importance increased dramatically
as the Turks threatened Vienna. By the help of treachery the Turks could
capture Gyar, but their rule lasted only 4 years. Legend has it that after
capturing Gyar the Turks put an iron rooster and half moon on the tower
of the castle, saying that Hungarians will recapture the town only when
the rooster crows and the half moon becomes full. The Hungarian general
Pallfy Miklos used this legend and took back the castle by ruse. This is how
the iron rooster became part of the city arms. In 1809 Emperor Napoleon,
after defeating the Austro-Hungarian army near Gyar blasted the bastions
of the castle, and it has never been rebuilt. From the 18th century a
robust economic prosperity characterised the town. By the 19th century
only Budapest surpassed Gyar as a Hungarian grain marketing centre. But
industry soon eclipsed trade as the economic strong-point, and today the
city is best known as a manufacturer of trains and trucks.
As befits a dynamic city of more than 125,000 people, Gyar is pervaded
by modern buildings, though the historical monuments are all around. Out
standing among the eye-catching new structures is the Kisfaludy Theatre,
named after the local poet and playwright Karoly Kisfaludy. It is the home
of the highly regarded Gyar ballet company, which specialized in modern
dance. The Cathedral was founded in the 11th century, but many builders
had a hand in working on it during its long and turbulent history. The
essentially Gothic church was rebuilt in Baroque style in the 17th century,
the neo-classic facade was tacked on 200 years later and then the damage
incurred during World War II had to be repaired. The chapel dedicated
x Gyor. The Conference Venue
to St. Ladislas, among the oldest parts of the cathedral, contains a reli
quary considered a masterpiece of Hungarian goldsmith's art. Other works
of gold, silver, copper and enamel, as well as ceremonial vestments, can
be seen in the cathedral's treasury. All around the cathedral, the winding
streets of the area called Chapter Hill are full of historic atmosphere as
well as the medieval keep, the Bishop's Palace, and remains of the town
bastions along the river. The Carmelite Church is a Baroque achievement
of the early 18th century. The gracefully proportioned facade has statues
in three niches and a large window in the organ loft. Rich paintings and
carvings decorate the interior. The Town Hall is aU-shaped, neobaroque,
turreted building. Strolling through the historic heart of the town today, in
pedestrians-only streets plentifully supplied with outdoor cafes, you might
well agree with the local promoters that it all turned out rather nicely in
the end.
