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This subtopic introduces the core ideas in limit theorems, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Central limit and other weak theorems. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
Large deviations. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
Strong theorems. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
Functional limit theorems; invariance principles. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
Zero-one laws. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
$L^p$-limit theorems. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.
None of the above. This topic studies limit theorems in probability, including convergence modes and asymptotic distributional behavior.
Wikipedia: Central limit theorem
Used to justify asymptotic approximations and large-sample behavior in stochastic models.