Chapter 1: Probability and Measure

mho1
Flashcards by mho1, updated more than 1 year ago
mho1
Created by mho1 over 5 years ago
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Masters Stochastic Processes and FInance Flashcards on Chapter 1: Probability and Measure, created by mho1 on 06/06/2015.
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\sigma-algebra
probability measure
measurable function
random variable/random vector
probability law/probability distribution
cumulative distribution function
probability density function
random variables X and Y are identically distributed if...
sub-\sigma-algebra
independent (\sigma-algebra)
independence (random variables)
Lebesgue integration Step 1: Indicator functions
Lebesgue Integration Step 2: simple functions
Lebesgue Integration Step 3: non-negative random variables
Lebesgue Integration Step 4: arbitrary random variables
integrable
null set
Proof - see lecture notes
Properties of the integral (five) linearity domination triangle inequality set bounded integrability change of variable
Properties of the Integral/Expectation 1. Linearity
Properties of the Integral/Expectation 2. Domination
Properties of the Integral/Expectation 3. the triangle inequality
Properties of the Integral/Expectation 4. Set bounded integrability
Properties of the Integral/Expectation 5. Change of variable
Dominated Convergence Theorem
Monotone Convergence Theorem
nth moment mean variance
moment generating function
Almost sure convergence
mean square convergence
Chebychev's Inequality
Cauchy-Schwarz inequality
convex function
Jensen's inequality
Proof - see notes
Absolutely Continuous measure Equivalent measures
Radon-Nikodym
Radon-Nikodym derivative
stochastic process
integrable stochastic process
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