Ricerc@Sapienza

In the last decades the climate change and other complex systems presented new challanges to forecast extreme natural events, these need new stochastic models and statistic tools in order to be modelled and simulated. Furthermore, many complex systems show the property of long-memory: the past times have a not negligible effect on the current time. Some examples can be provided by earthquakes, stock markets and Pm pollution.
The fractional processes in time or in space are able to describe such extreme events thanks to their densities' fat tails but the way in which the long-memory can be defined is still an open problem.
Indeed, mathematically, these characteristics can be expressed by the long-range dependence and the selfsimilarity property: the long range dependence expresses the correlation of the values the system takes in two distant times whereas the selfsimilarity explains the dynamic itself of the system for two distant time. Specifically, each property can be summarize by one parameter provided in each definition.
In order to make these definitions useful for applied sciences, estimators will be defined so that scientists can apply these statistical tools to get the parameters which describe long range dependence and selfsimilarity.