The theory of stochastic partial differential equations (SPDEs) emerged about thirty years ago and since then, it has been undergoing a dramatic development. This new field of mathematics is at the crossroad of probability and analysis, combining tools from stochastic analysis and the classical theory of partial differential equations. Motivations for the study of SPDEs arise both within mathematics, as well as from applications to other scientific settings possessing an inherent component of randomness. This randomness can be, for example, in the initial conditions, in the environment, or as an external forcing.
In the lecture, I will describe the mathematical approach to the most fundamental problems in the theory of SPDEs. For example, the underlying stochastic calculus, existence and uniqueness of solutions, and the properties of their sample paths. Aiming to be accessible to an audience ranging from graduate students to researchers not necessarily in the field of probability, the lecture will be of colloquium style, insisting on ideas rather than in technical details.
Marta Sanz-Solé is Professor at Universitat de Barcelona. Her research interests are in stochastic analysis, in particular stochastic differential and partial differential equations. Professor Sanz-Solé was awarded with a Narcis Monturiol Medal of Scientific and Technological Excellence by the Generalitat of Catalonia in 1998. She was elected Fellow of the Institute of Mathematical Statistics and was President of the European Mathematical Society from 2011-2014.
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