No abstract

No abstract

No abstract

We adopt the multilevel Monte Carlo method introduced by M. Giles (Multilevel Monte Carlo path simulation, Oper. Res. 56(3):607-617, 2008) to SDEs with additive fractional noise of Hurst parameter H > 1/2. For the approximation of a Lipschitz functional of the terminal state of the SDE we construct a multilevel estimator based on the Euler scheme. This estimator achieves a prescribed root mean square error of order ε with a computational effort of order ε −2 .

Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the formare established.

No abstract

Dedictated to Ludwig Arnold on the occasion of his 65th birthdayWe consider the two-step bifurcation scenario which has been studied by L. Arnold and his co-workers. We formulate a "continuous case" and a "measurable case" of the scenario, and present results and conjectures regarding sufficient conditions that it take place.

We propose and validate a new method for the evaluation of seismic hazard. In particular, our aim is to model large earthquakes consistently with the underlying geophysics. Therefore we propose a non-Poisson model, which takes into account occurrence history, improved with some physical constraints. Among the prevalent non-Poisson models, we chose the Markov renewal process, which is expected to be sufficient to capture the main characteristics, maintaining simplicity in analysis. However, due to the introduction of some physical constraint, our process differs significantly from others already presented in literature. A mixture of exponential + Weibull distributions is proposed for the waiting times and their parameters are estimated following the likelihood method. We validated our model, using data of earthquakes of high severity occurred in Turkey during the 20 th century. Our results exhibit a good accordance with the real events.