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Probability Space
Last updated Nov 1, 2022
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A Submartingale has uniformly Bounded First Moment iff it has uniformly Bounded Positive Moment
Adapted Process
Almost Sure Convergence
Almost Sure Convergence does not imply Lp Convergence
Alternate Option for CE
Baby Skorohod Theorem
Bayes Theorem
Centered Random Variable
Characteristic Function
Characteristic Function of Standard Gaussian Random Variable
Characteristic Function of a Gaussian Random Variable
Classification Problem
Upcrossings
Conditional Expectation
Conditional Expectation Exists and is Almost Surely Unique
Conditional Expectation is Linear
Conditional Expectation is Non-Decreasing
Conditional Expectation over the Trivial Sigma Algebra is Expectation
Conditional Expectation with respect to Random Element
Conditional Expectation with respect to Sigma Field
Conditional Expectation with respect to a Set is Integral divided by Probability
Conditional Probability
Conditioning on known information is Idempotent
Construction of Brownian Motion
Continuity Theorem
Continuous Support of a Random Variable
Convergence Almost Surely does not imply convergence of moments
Convex Sets contain their Expectation
Discrete Support of a Random Element
Discrete-Time Filtration
Distribution
Dot Product of Random Vector and Independent Entry Random Vector
Expectation
Expectation does not always exist
Expectations of a Martingale are Constant
Expectations of a Submartingale are Non-Decreasing
Expectations of a Supermartingale are Non-increasing
Filtration
Gaussian Random Variable
Independence
Kolmogorov Convergence Criterion
Kolmogorov Strong Law of Large Numbers
Kolmogorov Three Series Theorem
Law
Levy's Theorem
Markov Process
Martingale
Martingale Convergence Theorem
Nonnegative Bounded Strategy on Submartingale is a Submartingale
Nonnegative Bounded Strategy on Supermartingale is a Supermartingale
Partial Converse of Borel-Cantelli Lemma
Random Variable
Regular Conditional Distribution
Regular Conditional Probability
Smoothing
Standard Gaussian Random Variable
State Space
Stochastic Process
Strategy
Strategy Corresponding to a Stopping Time
Submartingale
Sum of Independent Random Variables is in L1 if and only if Random Variables are in L1
Supermartingale
Support of a Random Element
Trajectory
Uniform Integrability
Upcrossing Inequality
Upcrossing Strategy
Interactive Graph