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.
Une loi du logarithme itéré pour les martingales locales multidimensionnelles et son application en régression linéaire stochastique
Une remarque sur la convergence des martingales à deux indices
Une remarque sur le schéma de Bernoulli et quelques extensions
Upper bound of a volume exponent for directed polymers in a random environment
Vitesse de dispersion pour une classe de martingales
Weak compactness and convergence in two-parameter martingale Hardy spaces and the dual of the VMO space.
Weak type estimates associated to Burkholder's martingale inequality.
Weak Type Inequality for the Square Function of a Nonnegative Submartingale
Let f be a nonnegative submartingale and S(f) denote its square function. We show that for any λ > 0, , and the constant π/2 is the best possible. The inequality is strict provided ∥f∥₁ ≠ 0.
Абсолютная непрерывность и сингулярность локально непрерывных вероятностных распределений. II
Квадратическая вариация и сходимость случайных последовательностей
Мартингальные неравенства в симметричных пространствах
Мартингальные преобразования и равномерно сходящиеся ортогональные ряды
Производящие функции для К-ых рекордных моментов - мартингальный подход