It is well-known that Kolmogorov’s inequality is the particular case bk = 1, for all k and n = 1 in (1.1). Afterwards this inequality was extended to real valued martingales (see [4]). Since then, this inequality has been studied by many authors. For the case of R-valued random variables, Sung [22] obtained the Hájek-Rényi inequality for the associated sequence. Liu et al. [19] considered the n...

We show norm estimates for the sum of independent random variables in noncommutative Lp-spaces for 1 < p <∞ following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case. Among applications, we derive an equivalence for the p-norm of the singular values of a random matrix with independent entries, and characterize those symmetric subspaces an...

This paper states that for financial markets with continuous filtrations, the minimax local martingale measure defined by Frittelli is equivalent to the objective measure for nondecreasing but not strictly increasing utility functions if it exists, provided the dual utility function satisfies some boundedness assumptions for the relative risk aversion, and there exists an equivalent local marti...

We consider the first passage percolation model on the Zd lattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F . Let a0,n be the passage time from the origin to (n, 0, · · · , 0). Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of a0,n from its mean using different me...

Key advances include jumps in the availability of rich streams of data, precipitous drops in the cost of storing and retrieving massive amounts of data, exponential increases in computing power and memory, and jumps in the prowess of methods for performing machine learning and reasoning. These advances have come together to create an inflection point in our ability to harness large amounts of d...

We consider a mass-conservative fragmentation of the unit interval. The main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale which arises naturally in this setting, and a class of Lévy processes constrained to stay in a finite interval.

In the database framework of Kanellakis et al. it was argued that constraint query languages should meet the closed-form requirement, that is, they should take as input constraint databases and give as output constraint databases that use the same type of constraints. This paper shows that the closed-form requirement can be met for Datalog queries with Boolean equality constraints with double e...