Stochastic Processes and their Applications Proceedings of the Sympo
A volume of this nature containing a collection of papers has been brought out to honour a gentleman - a friend and a colleague - whose work has, to a large extent, advanced and popularized the use of stochastic point processes. Professor Srinivasan celeb
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M. J. Beckmann M. N. Gopalan R. Subramanian (Eds.)
Stochastic Processes
and their Applications Proceedings of the Symposium held in honour of Professor S. K. Srinivasan at the Indian Institute of Technology Bombay, India, December 27-30, 1990
Springer-Verlag Berlin Heidelberg GmbH
Editors M. J. Beckmann Brown University Providence, RI 02912, USA and Institut fUr Angewandte Mathematik Technische Universităt MUnchen MUnchen, FRG M. N. Gopalan Department of Mathematics Indian Institute of Technology Bombay, India R. Subramanian Department of Mathematics Indian Institute of Technology Madras, India
This Symposium was sponsored by the Indian Society for Probability and Statistics
ISBN 978-3-540-54635-1 ISBN 978-3-642-58201-1 (eBook) DOI 10.1007/978-3-642-58201-1 This work is subject to' copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication Of parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1991 Originally published by Springer-Verlag Berlin Heidelberg New York in 1991 Typesetting: Camera ready by author 42/3140-543210 - Printed on acid-free paper
PROFESSOR S. K. SRINIVASAN
CONTENTS Preface
Scientific Publications of Professor S.K.Srinivasan
Books
IX XI XIV XVII
Scientific Publications of Professor S.K.Srinivasan
Research Papers
XVI II
Biographical Sketch of Professor S.K.Srinivasan Scientific Contributions of Professor S.K.Srinivasan
Keynote Address in the Symposium :
S.K.Srinivasan : Fifty Years of Cascade Theory:
XXV II I
Stochastic Methods and Their Ramifications I.Stochastic Theory Marcel F.Neuts: The Square Wave Spectrum of a Markov Renewal Process Ann-Lee Wang. David Vere-Jones and Xiao-gu Zheng:
Simulation
and
Estimation Procedures for Stress Release Models
11
2. Physics J. Bass: Positive Definite Functions in Quantum Mechanics and in 28
Turbulence J.Jeffers
and
T.J.Shepherd:
Population
Monitoring
and
the
Quantum Input-Output Formalism
44
P.M.Mathews : An Application of the Kalman Filter in Geoastronomy
53
K.V.Parthasarathy: Conformal Martingales in Stochastic Mechanics
62
E.C.G.Sudarshan : Probability Distributions Over Noncommuting Variables
69
R.Vasudevan: Stochastic Quantum Mechanics
82
3.Biology George Adomian, Matthew Witten and Gerald E. Adomian:A New Approach to the Solution of Neurological Models: Application to the Hodgkin-Huxley and
the Fi tzhugh-Nagumo Equat ions
99·
A.V.Holden and M.A. Muhamad ; Neuronal Variability; Stochasticityor Chaos?
114
A.Rangan : A Limit Theorem and Asymptotical Statistical Characteristics a Selective Intera.;t;.on Model of a S
