A Signed Measure on Path Space Related to Wiener Measure

Measure invariance on the Lie-Wiener path space

In this paper we extend some recent results on moment identities, Hermite polynomials, and measure invariance properties on the Wiener space, to the setting of path spaces over Lie groups. In particular we prove the measure invariance of transformations having a quasi-nilpotent covariant derivative via a Girsanov identity and an explicit formula for the expectation of Hermite polynomials in the...

A novel fuzzy measure and its extensional signed fuzzy measure

When there are interactions among the independent variables, the performances of the most often used multiple regression models and ridge regression model are not well enough. In contrast, the Choquet integral takes into account the interactions among independent variables, the discrete Choquet integral regression models based on some non-negative valued fuzzy measures or monotonic measure can ...

Wiener measure and Donsker’s theorem

How to Measure Path Length ?

Path length measuring is a relevant engineering problem. Leonardo Da Vinci designed for the military appropriate equipment, the podometer, to do so. Modern equipment such as step meters and map meters are quite similar to Da Vinci‟s design, despite geometrical statistical stereological methods based on theorems of Cauchy and Buffon that were potentially available for a long period of time for d...

A Survey on Stability Measure of Networks

In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity.