The Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale Analogues

Inequalities; stochastic orderings (60E15) Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44)

Cites Work

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The first passage time problem over a moving boundary for asymptotically stable Lévy processes
A martingale approach in problems on first crossing time of nonlinear boundaries
Boundary-crossing identities for diffusions having the time-inversion property
Distribution function inequalities for martingales
On the \(L^p\) norms of stochastic integrals and other martingales
The sharp constant for the Burkholder-Davis-Gundy inequality and non-smooth pasting
Crossing an asymptotically square-root boundary by the Brownian motion
On the integrability of the martingale square function
Extrapolation and interpolation of quasi-linear operators on martingales
Change of Time and Change of Measure
Sharp maximal inequalities for the martingale square bracket
Sharp Martingale and Semimartingale Inequalities
The Crossing Time of a One-Sided Nonlinear Boundary by Sums of Independent Random Variables
The Best Bound in the L logL Inequality of Hardy and Littlewood and its Martingale Counterpart
One-Sided Boundary Crossing for Processes with Independent Increments
Brownian first exit from and sojourn over one sided moving boundary and application
On Conditions for Uniform Integrability of Continuous Non-Negative Martingales
On Discontinuous Martingales
Martingales, Tauberian Theorem, and Strategies of Gambling
On Maximal Inequalities for Purely Discontinuous Martingales in Infinite Dimensions
On an Identity for Stochastic Integrals
When a Stochastic Exponential Is a True Martingale. Extension of the Beneš Method
Concentration Inequalities for Sums and Martingales
Optimal Stopping Rules
On the Decomposition of Continuous Submartingales
Martingale Integrals
A First Passage Problem for the Wiener Process
ON CONTINUOUS MARTINGALES
Changes of time, stochastic integrals, and weak martingales
On Moment Inequalities for Stochastic Integrals
On Stopping Times for a Wiener Process
Probability-2
Sequential Tests of Statistical Hypotheses
Maximal inequalities and some applications

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