Limit theorems for vertex-reinforced jump processes on regular trees.
The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well-known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample covariance matrix. In a recent article Bryc, Dembo and Jiang [Ann. Probab.34 (2006) 1–38] establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the...
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.
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.
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.
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...