Foundations of Quantitative Finance, Book VI: Densities, Transformed Distributions, and Limit Theorems [Hardcover]

1 Density Functions

1.1 Density Functions of Measures

1.2 Density Functions of Distributions

1.2.1 Distribution Functions and Random Vectors

1.2.2 Distribution Functions and Probability Measures

1.2.3 Existence of Density Functions

1.3 Marginal Density Functions

1.4 Densities and Independent RVs

1.5 Conditional Density Functions

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2 Transformations of Random Vectors

2.1 Cavalieri.s Principle

2.2 Sums of Independent Random Vectors

2.2.1 Distribution Functions

2.2.2 Density Functions

2.3 A Result on Convolutions

2.4 Ratios of Independent Random Variables

2.5 Densities of Transformed Random Vectors

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3 Weak Convergence of Probability Measures

3.1 Portmanteau Theorem on R

3.2 Portmanteau Theorem on Rm

3.3 Applications

3.3.1 The Mapping Theorem

3.3.2 Mann-Wald Theorem

3.3.3 Cram?r-Wold Theorem - Part 1

3.3.4 Slutsky.s Theorem

3.3.5 The Delta Method

3.3.6 Sche??.s Theorem

3.3.7 Prokhorov.s theorem

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4 Expectations of Random Variables 2

4.1 Expectations and Moments

4.1.1 Expectations of Independent RV Products

4.1.2 Moments and the MGF

4.1.3 Properties of Moments

4.2 Weak Convergence and Moment Limits

4.3 Conditional Expectations

4.3.1 Conditional Probability Measures

4.3.2 Conditional Expectation -An Introduction

4.3.3 Conditional Expectation as a Function&l“