Continuous Mapping Theorem: Probability Theory, Continuous Function, Convergence of Random Variables, Portmanteau Theorem, Closure (topology). - Softcover

 
9786133791138: Continuous Mapping Theorem: Probability Theory, Continuous Function, Convergence of Random Variables, Portmanteau Theorem, Closure (topology).

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the continuous mapping theorem states that continuous functions are limit- preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g (xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→†with one of the types of convergence of random variables.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the continuous mapping theorem states that continuous functions are limit- preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g (xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→†with one of the types of convergence of random variables.

"About this title" may belong to another edition of this title.