Maximum likelihood estimation (MLE) of stochastic differential equations (SDEs) is difficult because in general the transition density function of these processes is not known in closed form, and has to be approximated somehow. An approximation based on efficient importance sampling (EIS) is...

The non-stationary gamma process is a non-decreasing stochastic process with independent increments. By this monotonic behavior this stochastic process serves as a natural candidate for modelling time-dependent phenomena such as degradation. In condition-based maintenance the first time such a...

The Poisson distribution, in general remains sensitive to small departure of frequencies especially at the right tail of the distribution. In many situations it may happen that the Generalized Poisson Distribution (GPD) or a compound distribution provides a closer fit to a frequency distribution...

This paper deals with the main theoretical problems regarding the application of stochastic processes to leptokurtic financial return distributions. A sort of statistical tests based on the stock index Banamex 30 is performed in order to choose the stochastic model that provide the best fit to...

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the...

We define the local empirical process, based on n i.i.d. random vectors in dimension d, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that for these local empirical processes, indexed by classes of sets that vary with n and...

It is shown that for elliptically distributed bivariate random vectors, the riskiness and dependence strength of random portfolios, in the sense of the univariate convex and bivariate concordance stochastic orders respectively, can be simply characterised in terms of the vector's...