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.
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© 1995 Springer Science+Business Media New York
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Borkar, V.S. (1995). Foundations of Continuous-Time Processes. In: Probability Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0791-7_6
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DOI: https://doi.org/10.1007/978-1-4612-0791-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94558-3
Online ISBN: 978-1-4612-0791-7
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