In most real life applications Mathematics not only face the challenge of modeling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design. And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art…
What links gas molecules, charged particles, bacteria and fish? Partial differential equations help us understanding their collective behaviour. Kinetic modelling allows for a multi-scale strategy in a number of important applications in science and technology. Mean field limits and kinetic descriptions have become one of the most powerful tools in applied mathematics to bridge microscopic and…
In this talk, we are concerned with the expected values of certain functionals of the path of a stochastic process during a given time period. High-order asymptotic characterizations of such values when the time period shrinks to 0 have a wide range of applications. In statistics, they are crucial in obtaining the infill asymptotic properties…
Recently, there has been an increasing interest from the community in real-life complex system modeling. The most popular example is provided by systems where the number of agents is so large, that only a statistical description (reminiscent to the statistical mechanics description of systems in thermodynamics) turns out to be viable. The usual way to…