Chap. 5 Stochastic convergence concepts and classical limit theorems

1 fevereiro 2022, 12:00 • Manuel Cabral Morais

5.8 Characteristic functions

5.9 The Central Limit Theorem

[5.10 The law of the iterated logarithm

5.11 Applications of the limit theorems]

E/C: 5.155 (Exp), 5.162(b, hints), 5.181(a)

Obs.: Topics 5.10 and 5.11 were browsed very quickly…    

Chap. 5 Stochastic convergence concepts and classical limit theorems

1 fevereiro 2022, 09:00 • Manuel Cabral Morais

5.3 Convergence under transformations

5.3.2 Algebraic operations (from the table after Challenge 5.92 until the end of the subsection)

[5.4 Convergence of random vectors]

5.5 Limit theorems for Bernoulli summands

5.5.1 Laws of large numbers for Bernoulli summands

5.5.2 Central limit theorems for Bernoulli summands

5.5.3 The Poisson limit theorem

5.6 Weak law of large numbers

5.7 Strong law of large numbers

E/C: -;   5.108(a); -; 5.121;   5.129;    5.144;

Obs.: Topic 5.4 was browsed very quickly…    

Chap. 5 Stochastic convergence concepts and classical limit theorems

31 janeiro 2022, 13:30 • Manuel Cabral Morais

5.1 Modes of convergence

5.1.2 Convergence in distribution (from Challenge 5.35 until the end of the subsection)

5.1.3 Alternative criteria

5.2 Relationships among the modes of convergence

5.2.1 Implications always valid

5.2.2 Counterexamples

5.2.3 Implications of restricted validity

5.3 Convergence under transformations

5.3.1 Continuous mappings

5.3.2 Algebraic operations (until the table after Challenge 5.92)

MAP30 #4

25 janeiro 2022, 12:00 • Manuel Cabral Morais

MAP30 #4; discussion of its detailed solution

Chap. 5 Convergence concepts and classical limit theorems

25 janeiro 2022, 09:00 • Manuel Cabral Morais

5.1 Modes of convergence

5.1.1 Convergence of r.v. as functions on Omega (from Example 5.3 until the end of the subsection)

5.1.2 Convergence in distribution (until Example 5.33)