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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …