Category Archives: convergence

Spaces and Convergences

Metric spaces: a set where a notion of distance (called a metric) between elements of the set is defined. Vector spaces or Linear space: a mathematical structure formed by a collection of vectors. Normed vector spaces: a Vector space with … Continue reading

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Convergence in Probability and Convergence with Probability 1

Definations: For a random vector and a sequence of random vectors defined on a probability space . 1. Convergence in Probability or Convergence of probability measures, is kind of convergence in measure, in concept of the measure theory. : for … Continue reading

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Stochastic o and O symbols

Stochastic and symbols are the basic symbols for Asymptotic Statistics or Large Sample Theory. (i) : if . sequence of random variables is of smaller order in probability than a sequence . In particular, , “small oh-P-one”, if and only … Continue reading

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Why the limit of the sequence 1/n is 0?

We know that one of the basic facts in mathematical analysis is . My question is why, the sequence , which is for any , finally equals to 0 as ? Yes, that’s the definition of limits. What I will say here is … Continue reading

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