Stochastic Processes and their Applications

1. Front Matter

   Pages I-XLI

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2. Stochastic Theory

   1. The Square Wave Spectrum of a Markov Renewal Process

      • Marcel F. Neuts

      Pages 1-10

   2. Simulation and Estimation Procedures for Stress Release Model

      • Ann-Lee Wang, David Vere-Jones, Xiao-gu Zheng

      Pages 11-27

3. Physics

   1. Positive Definite Functions in Quantum Mechanics and in Turbulence

      • J. Bass

      Pages 28-43

   2. Population Monitoring and the Quantum Input-Output Formalism

      • J. Jeffers, T. J. Shepherd

      Pages 44-52

   3. An Application of the Kalman Filter in Geoastronomy

      • P. M. Mathews

      Pages 53-61

   4. Conformal Martingales in Stochastic Mechanics

      • K. V. Parthasarathy

      Pages 62-68

   5. Probability Distributions over Noncommuting Variables

      • E. C. G. Sudarshan

      Pages 69-81

   6. Stochastic Quantum Mechanics

      • R. Vasudevan

      Pages 82-98

4. Biology

   1. A New Approach to the Solution of Neurological Models: Application to the Hodgkin-Huxley and the Fitzhugh-Nagumo Equations

      • George Adomian, Matthew Witten, Gerald E. Adomian

      Pages 99-113

   2. Neuronal Variability — Stochasticity or Chaos?

      • A. V. Holden, M. A. Muhamad

      Pages 114-126

   3. A Limit Theorem and Asymptotical Statistical Characteristics for a Selective Interaction Model of a Single Neuron

      • A. Rangan

      Pages 127-133

   4. Phase Dependent Population Growth Models

      • C. R. Ranganathan

      Pages 134-144

5. Operations Research

   1. The Optimal Investment Process in German Industry

      • Horst Albach

      Pages 145-161

   2. Incentives and Regulation in Queues

      • Kashi R. Balachandran

      Pages 162-176

   3. Two Models of Brand Switching

      • Martin J. Beckmann

      Pages 177-187

   4. Stochastic Processes: Use and Limitations in Reliability Theory

      • A. Birolini

      Pages 188-210

   5. Stochastic Processes and Optimization Problems in Assemblage Systems

      • Franz Ferschl

      Pages 211-221

   6. A Software Package Tool for Markovian Computing Models with Many States: Principles and its Applications

      • Satoshi Fukumoto, Shunji Osaki

      Pages 222-231

   7. Reliability Assessment Measurement for Redundant Software Systems

      • Jun Hishitani, Shigeru Yamada, Shunji Osaki

      Pages 232-240

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 celebrated his sixt~ first 1:!irth d~ on December 16,1990 and will be retiring as Professor of Applied Mathematics from the Indian Institute of Technolo~, Madras on June 30,1991. In view of his outstanding contributions to the theor~ and applications of stochastic processes over a time span of thirt~ ~ears, it seemed appropriate not to let his birth d~ and retirement pass unnoticed. A s~posium in his honour and the publication of the proceedings appeared to us to be the most natural and sui table ~ to mark the occasion. The Indian Societ~ for ProbabU it~ and Statistics volunteered to organize the S~posium as part of their XII Annual conference in Bomba~. We requested a number of long-time friends, colleagues and former students of Professor Srinivasan to contribute a paper preferabl~ in the area of stochastic processes and their applications. The positive response and the enthusiastic cooperation of these distinguished scientists have resulted in the present collection. The contributions to this volume are divided into four parts: Stochastic Theor~ (2 articles), P~sics (6 articles), Biolo~ (4 articles) and Operations Research (12 articles). In addition the ke~note address delivered b~ Professor Srinivasan in the S~posium is also included.

• Markov renewal process
• Martingale
• Operations Research
• Quantenmechanik
• Quantum Mechanics
• Simulation
• Stochastic Theory
• Stochastic processes
• Stochastische Theorie
• calculus
• optimization
• point process
• stochastic process
• turbulence

• Brown University, Providence, USA

  M. J. Beckmann

• Institut für Angewandte Mathematik, Technische Universität München, München, Germany

  M. J. Beckmann

• Department of Mathematics, Indian Institute of Technology, Bombay, India

  M. N. Gopalan

• Department of Mathematics, Indian Institute of Technology, Madras, India

  R. Subramanian

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