Markov's inequality for random variables

Depends on

• Expectation of a nonnegative or integrable random variable
• Chebyshev-Markov inequality for the integral

Used by

• Chebyshev's inequality for random variables Corollary
• Common drift and minorization give containment under diminishing adaptation, strong aperiodicity, and a finite initial V-moment Corollary
• Boundedness of first moments alone does not give uniform integrability Counterexample
• Diminishing adaptation and uniform ergodicity need not give a strong law Counterexample
• Pointwise resampling misses the long-run variance of an AR(1) mean Counterexample
• A finite identifiable model with posterior consistency Example
• Markov and Chebyshev sharpness Example
• Normal location fitted under the wrong variance Example
• Tightness from a uniform moment bound Example
• A bounded-density Gaussian bridge has a Borel multiscale law Lemma
• A one-sided DQM path yields an iid LAN proxy Lemma
• A variance-sensitive bound for bounded empirical suprema Lemma
• Adjacent iid vector functionals admit a finite-moment strong approximation Lemma
• Bernstein tail bound for independent bounded sums Lemma
• Bounded independent matrix Bernstein bound from the trace exponential Lemma
• Bounded independent vector rows admit a logarithmic cubed Gaussian coupling Lemma
• Bracketing entropy implies empirical-process asymptotic equicontinuity Lemma
• Common drift and strongly aperiodic minorization give a uniform geometric bound Lemma
• Compact-uniform LAN approximates compact-prior posteriors Lemma
• Conditional CLT for independent resampled weighted blocks Lemma
• Countably partitioned sieves yield posterior contraction by weighted entropy Lemma
• Exact block budget for the covariance geometric-median pilot Lemma
• Exponential averaged spectral projectors for a finite cq ensemble Lemma
• Exponential tests and KL mass force posterior exclusion Lemma
• Finite Dirichlet gamma representation and weighted Bernstein bound Lemma
• Finite moments control increments over short moving windows Lemma
• Finite-horizon SMC empirical laws converge for integrable tests Lemma
• Heterogeneous bounded atom vector rows admit a logarithmic cubed Gaussian coupling Lemma
• Independent Brownian motion straightens a Poisson clock Lemma
• Linear and quadratic Gaussian statistics have exponential tails Lemma
• Normalized product likelihood expansion under QMD Lemma
• Squared-norm concentration for real and normalized complex Gaussians Lemma
• Strong Brownian approximation implies overlapping-batch consistency Lemma
• Tests and a sieve tail imply posterior contraction from a denominator bound Lemma
• The posterior excludes large scales and mixing mass far from compact data Lemma
• Type-S posterior contracts in quotient log-density coordinates without a tail restriction on a log-Lipschitz prior Lemma
• Uniform finite-horizon moments for tamed Euler approximations Lemma
• Weighted overlapping-block moment and covariance limits Lemma
• Correct-scale slab bound for multivariate trimming Proposition
• The general inequalities compare cleanly with the published finite ones Remark

…and 31 more results.

Dependency tree · two levels

10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Rick Durrett, Probability: Theory and Examples, 5th ed., Section 1.6.1 (standard reference, not scraped)
• J. R. Norris, Probability and Measure, Section 4.2 (standard reference, not scraped)