Maximal inequalities and some applications
F Kühn, RL Schilling - Probability Surveys, 2023 - projecteuclid.org
A maximal inequality is an inequality which involves the (absolute) supremum sup s⩽ t| X s|
or the running maximum sup s⩽ t X s of a stochastic process (X t) t⩾ 0. We discuss maximal …
or the running maximum sup s⩽ t X s of a stochastic process (X t) t⩾ 0. We discuss maximal …
Moderate maximal inequalities for the Ornstein-Uhlenbeck process
The maximal inequalities for diffusion processes have drawn increasing attention in recent
years. Here we prove the moderate maximal inequality for the Ornstein-Uhlenbeck process …
years. Here we prove the moderate maximal inequality for the Ornstein-Uhlenbeck process …
Sharp maximal inequalities for stochastic processes
YA Lyulko, AN Shiryaev - Proceedings of the Steklov Institute of …, 2014 - Springer
This work is a survey of existing methods and results in the problem of estimating the
mathematical expectation of the maximum of a random process up to an arbitrary Markov …
mathematical expectation of the maximum of a random process up to an arbitrary Markov …
On a certain exponential inequality for Gaussian processes
C Borell - Extremes, 2006 - Springer
If X=(X j) j= 1 m is a zero-mean Gaussian stochastic process and σ_j=\left(E\bigX_j^2\big\
right)^1/2, j= 1,..., m, Tsirel'son (Theory Probab. Appl., 30, 820–828, 1985) and more …
right)^1/2, j= 1,..., m, Tsirel'son (Theory Probab. Appl., 30, 820–828, 1985) and more …
On suprema of Lévy processes and application in risk theory
R Song, Z Vondraček - Annales de l'IHP Probabilités et statistiques, 2008 - numdam.org
Let ̂X= C− Y where Y is a general one-dimensional Lévy process and C an independent
subordinator. Consider the times when a new supremum of ̂X is reached by a jump of the …
subordinator. Consider the times when a new supremum of ̂X is reached by a jump of the …
On maximal inequalities for stable stochastic integrals
A Joulin - Potential Analysis, 2007 - Springer
Sharp maximal inequalities in large and small range are derived for stable stochastic
integrals. In order to control the tail of a stable process, we introduce a truncation level in the …
integrals. In order to control the tail of a stable process, we introduce a truncation level in the …
Martingales with given maxima and terminal distributions
RP Kertz, U Rösler - Israel Journal of Mathematics, 1990 - Springer
Let μ be any probability measure on R with λ| x| d μ (x)<∞, and let μ* denote its associated
Hardy and Littlewood maximal pm It is shown that for any pm v for which μ< ν< μ* in the …
Hardy and Littlewood maximal pm It is shown that for any pm v for which μ< ν< μ* in the …
[PDF][PDF] A note on maximal inequalities
J Pitman - Séminaire de probabilités de Strasbourg, 1981 - numdam.org
1. Introduction According to the L2 maximal inequality of Doob [3], for a martingale (1.1) And
an inequality of Newman and Wright [9] states that (1) holds (with constant 2 instead of 4) if …
an inequality of Newman and Wright [9] states that (1) holds (with constant 2 instead of 4) if …
[PDF][PDF] Some inequalities for strong martingales
NE Frangos, P Imkeller - Annales de l'IHP Probabilités et statistiques, 1988 - numdam.org
We extend Walsh's maximal inequality for strong martin-gales to transforms of strong
martingales by bounded previsible processes and show that they converge as Using …
martingales by bounded previsible processes and show that they converge as Using …
[PDF][PDF] Maximal inequalities of the It^ o integral with respect to Poisson random measures or Lévy processes on Banach spaces
E Hausenblas - Potential analysis, 2011 - pure.unileoben.ac.at
Maximal Inequalities of the Itô Integral with Respect to Poisson Random Measures or Lévy
Processes on Banach Spaces Page 1 Potential Anal (2011) 35:223–251 DOI 10.1007/s11118-010-9210-0 …
Processes on Banach Spaces Page 1 Potential Anal (2011) 35:223–251 DOI 10.1007/s11118-010-9210-0 …