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Foundations of Continuous-Time Processes

  • Vivek S. Borkar
Part of the Universitext book series (UTX)

Abstract

This chapter introduces some basics of continuous time stochastic processes, mainly those concerning their construction and sample path properties. A detailed study of these processes is a vast enterprise and is well beyond the scope of this book. For simplicity, we shall restrict to real-valued processes on the time interval [0,1], that is, a family X t of real random variables on some probability space, indexed by the time variable t ∈ [0,1]. Much of what we do below extends to arbitrary time intervals and more general (e.g. Polish space-valued) processes with minor modifications.

Keywords

Sample Path Supremum Norm Continuous Version Complete Probability Space Real Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Vivek S. Borkar
    • 1
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia

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