The central limit problem for strictly stationary sequences [Abstract of thesis]
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The Hájek asymptotics for finite population sampling and their ramifications
The hyperharmonic numbers and the phratry of the coupon collector. (Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes.)
The Maximal (C, ...) Operator of Two-Parameter Walsh-Fourier Series.
The maximal variation of a bounded martingale and the central limit theorem
The Radon-Nikodym property and convergence of amarts in Frechet spaces
The Rate of Convergence in the Functional Central Limit Theorem for Random Quadratic Forms with Some Applications to the Law of Iterated Logarithm.
The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model
We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by . To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions...
Théorèmes limites avec poids pour les martingales vectorielles
Théorèmes limites avec poids pour les martingales vectorielles
We give limit theorems specifying weak and strong rates of convergence associated to a quadratic extension of the martingale almost-sure central limit theorem. Some typical examples are discussed to illustrate how to make use of them in statistic.
Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior
Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function
Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that 𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,..., 𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,.... The first inequality is sharp, and it is strict in all nontrivial cases.