Liftings for abstract valued functions and separable stochastic processes
In this paper we extend the notion of lifting from real-valued functions to abstract-valued functions (functions with values in a completely regular space). We prove the existence and uniqueness of the “abstract lifting” associated with a given “real lifting”. As an application we show that given a stochastic process with values in a completely regular space, the modification of this process obtained by applying a lifting is always separable.
KeywordsStochastic Process Probability Theory Mathematical Biology Regular Space Abstract Lift
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