Stochastic Analysis and Applications Proceedings of the Internationa
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Stochastic Analysis and Applications Proceedings of the International Conference held in Swansea, April 11-15, 1983
Edited by A. Truman and D. Williams
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editors Aubrey Truman David Williams Department of Mathematics and Computer Science University College of Swansea Singleton Park, Swansea SA2 8PR Wales
AMS Subject Classification (1980): 60H05, 60H10 ISBN 3-540-13891-9 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13891-9 Springer-Verlag New York Heidelberg Berlin Tokyo
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach / Bergstr. 2146/3140-543210
PREFACE
This volume contains a number of papers presented at the Workshop on Stochastic Analysis and its Applications, held in Swansea from 11 April to 15 April 1983, together with some more recent research papers by the Swansea school.
The applications include such diverse
topics as stochastic mechanics and the Titius-Bode law, non-standard Dirichlet forms and polymers, statistical mechanics, quantum stochastic processes, the applications of local-time to proving path-wise uniqueness of solutions of stochastic differential equations and its application to excursion theory, Bessel processes and pole-seeking Brownian motion, queues, potential theory and Wiener-Hopf theory. Some new results for Brownian motion on how one process determines another are also given.
The applications to Mathematical Physics
appear first, followed by the papers on local-time, Bessel processes and queues.
The papers of the Swansea school are collected together
at the end of the volume.
We are grateful to SERC for financial support
through research grant GR/C52162 and we are especially indebted to James Taylor for invaluable help and advice during the conference. Finally we should like to record our thanks to Mrs E. Williams, Mrs M. Prowse and Mrs M. Brook for making such an excellent job of typing the Swansea contributions.
A. Truman D. Williams Swansea April, 1983
TABLE OF CONTENTS S. ALBEVERIO, PH. BLANCHARD, R. H0EGH-KROHN, 'Newtonian diffusions and planets, with a remark on non-standard Dirichlet forms and polymers'. J.T. LEWIS, J.V. PULE, mechanics' •
'The equivalence of ensembles in statistical
· 25
F. PAPANGELOU, 'The uniqueness of regular DLR measures for certain one-dimensional spin systems. .
36
R.L. HUDSON, K.R. PARTHASARATHY,
45
'Generalised Weyl operators'.
J.F. LE GALL, 'One-dimensional stochastic differential equations involving the local-times of unknown processes'.
• 51
P. McGILL, 'Time chang
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