Probability theory and stochastic processes Foundations: probability spaces and events Concept
Probability space
Summary
A probability space is the mathematical model of a random experiment: a sample space, a σ-algebra of events and a probability measure on the events. The node probability space gives the precise definition.
Where this leads
39 pages build on this one.
- Filtration
- Random matrix
- Ergodic decomposition
- Koopman operator
- Lovász local lemma
- Standard probability space
- Measure space
- Stochastic Volterra equation
- Simple random sample
- Point process
- Kingman's subadditive ergodic theorem
- Kolmogorov automorphism
- Regular conditional probability
- Probabilistic method
- Local time
- Finite-dimensional distributions
- Random ordinary differential equation
- Mixing
- Integral operator
- Furstenberg's multiple recurrence theorem
- Infinite product measure
- Weak mixing
- Free probability
- Stochastic geometry
- Talagrand's concentration inequality
- Ergodic transformation
- Shannon–McMillan–Breiman theorem
- Janson inequality
- Birkhoff's ergodic theorem
- Kac's lemma
- Random integral equation
- Oseledets theorem
- Spectral theory of dynamical systems
- Coupling
- Maximal ergodic theorem
- Pesin theory
- Kolmogorov–Sinai entropy
- Stochastic differential equation
- Random dynamical system
Further reading
- Web https://en.wikipedia.org/wiki/Probability_space, lead section
About this page
| Tag | 0NFPJVJJHX |
|---|---|
| URI | m2://0NFPJVJJHX |
| Aliases | probability-triple |
| Kind | concept |
| Writing | W1 stated |
| MSC | 60A05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Used by
- Filtration
- Random matrix
- Koopman operator
- Lovász local lemma
- Standard probability space
- Measure space
- Simple random sample
- Point process
- Kingman's subadditive ergodic theorem
- Kolmogorov automorphism
- Regular conditional probability
- Probabilistic method
- Local time
- Finite-dimensional distributions
- Random ordinary differential equation
- Mixing
- Furstenberg's multiple recurrence theorem
- Infinite product measure
- Weak mixing
- Free probability
- Stochastic geometry
- Talagrand's concentration inequality
- Ergodic transformation
- Shannon–McMillan–Breiman theorem
- Janson inequality
- Birkhoff's ergodic theorem
- Kac's lemma
- Random integral equation
- Oseledets theorem
- Spectral theory of dynamical systems
- Coupling
- Maximal ergodic theorem
- Kolmogorov–Sinai entropy
- Stochastic differential equation
- Random dynamical system