Dr. G. Falsone
Dr. G. Falsone
Università degli Studi di Messina, Italy
Title: Non-Gaussian Stochastic differential calculus: an engineering perspective
In this work a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to non-Gaussian white noises is given. In this field, particular attention must be paid because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied if neither the Ito calculus nor the Stratonovich one is adopted. Here all the principal approaches, as treating this problem are analysed reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible. In particular, the Marcus approach is treated highlighting that it satisfies the classical differential rules and that it is possible to consider some correction terms respect to the Ito integration. Then, the Di Paola-Falsone method is also examined, being based on the classical differential rules on compound functions. Even this approach, that is used above in the engineering field, allows of defining some correction terms respect to the Ito calculus. The third approach here reported is the so-called (*)  calculus, that, using a completely different theoretical approach, arrives to analogous results.
Giovanni Falsone. He has accomplished his Degree in Civil Engineering cum laude from the University of Palermo and Research Doctorate (Ph.D.) in Structural Engineering from the University of Napoli. After having worked as Researcher at the University of Catania and as Associate Professor at the University of Messina, he is currently working as Full Professor of Structural Mechanics at the Engineering Department of the University of Messina. In the years interval 2004-2012 he was Head of the Department of Civil Engineering of the University of Messina. He has been author and co-author of more than 150 publications, of which more than 50 are articles on Scopus and Web of Science referred journals. His research topics are principally related to the application of the stochastic theory to some engineering problems, as the dynamics of linear and nonlinear systems subjected to delta-correlated inputs, the seismic reliability of structures, the homogenization of composite materials and the response characterization of uncertain structures. He is currently Member of the Editorial Boards of Mathematical Problems in Engineering (Hindawi PC) and of Journal of Advanced Engineering (IGRPS).