Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables.
Martingale criteria for stochastic stability
Martingale theorems in the ergodic theory
Maximal inequalities and some convergence theorems for fuzzy random variables
Some maximal inequalities for quadratic forms of independent and linearly negative quadrant dependent fuzzy random variables are established. Strong convergence of such quadratic forms are proved based on the martingale theory. A weak law of large numbers for linearly negative quadrant dependent fuzzy random variables is stated and proved.
Maximal inequalities for dependent random variables and applications.
Medidas de centralización multidimensionales (ley fuerte de los grandes números).
En este trabajo definimos una medida de centralización multidimensional para vectores aleatorios como el valor del parámetro para el que se alcanza el mínimo de las integrales de ciertas funciones. Estudiamos su relación con otras medidas de centralización multidimensionales conocidas. Finalizamos demostrando la Ley Fuerte de los Grandes Números, tanto para la medida de centralización definida como para la de dispersión asociada.
Metric results on a new notion of discrepancy
Milstein’s type schemes for fractional SDEs
Weighted power variations of fractional brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.
Models for option pricing based on empirical characteristic function of returns
The standard Merton-Black-Scholes formula for European Option pricing serves only as approximation to real values of options. More advanced extensions include applications of Lévy processes and are based on characteristic functions, which are more convenient to use than the corresponding probability distributions. We found one of the Lewis (2001) general theoretical formulae for option pricing based on characteristic functions particularly suitable for a statistical approach to option pricing. By...
Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages.
Moment functions and laws of large numbers on hypergroups.
Moment inequality for -mixing sequences and its applications.
Moments of passage times for Lévy processes
Moving Shift Averages for Ergodic Transformations.
Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments
Multidimensional version of the results of Komlos, Major and Tusnady for vectors with finite exponential moments
A multidimensional version of the results of Komlos, Major and Tusnady for the Gaussian approximation of the sequence of successive sums of independent random vectors with finite exponential moments is obtained.
Multiparameter pointwise ergodic theorems for Markov operators on L∞.
Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averagesAnf = (n + 1)-d Σ0≤ni≤n P1n1 P2n2 ... Pdnd f (n ≥ 0)converge almost everywhere if and only if there exists an invariant and equivalent finite measure λ for which the Radon-Nikodym derivative v = dλ/dμ is in the dual space Lp'(X,F,μ). Next we study the case in...