What is a continuous stochastic process? - Mathematics Stack Exchange So, there will be a discontinuity at time k Isn't this violating the definition of continuous stochastic process or is it that I have to keep ω ω constant throught out the process ? Also, is ω ω in the definition of continuous stochastic process the outcome at any point of time or is it the string of the outcomes that occurs till time
notation - Different types of sample spaces in probability . . . Continuous Models : Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not be sufficient to characterize the probability law Discrete probability law deals with finite sample spaces, but continuous probability models deal with continuous sample
Proving the inverse of a continuous function is also continuous 6 All metric spaces are Hausdorff Given a continuous bijection between a compact space and a Hausdorff space the map is a homeomorphism Proof: We show that f f is a closed map Let K ⊂E1 K ⊂ E 1 be closed then it is compact so f(K) f (K) is compact and compact subsets of Hausdorff spaces are closed Hence, we have that f f is a homeomorphism