Foundations of Continuous-Time Processes
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.
KeywordsSample Path Supremum Norm Continuous Version Complete Probability Space Real Random Variable
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