2019. április 23.
We kindly invite you to the Miklós Farkas Seminar
25 April (Thursday) 10.15, BME, H306
Mihály Kovács (Pázmány Péter Catholic University)
Introduction to the semigroup approach for stochastic partial differential equations and their finite element approximation
In part 1 of this talk I will give a short introduction to the operator semigroup approach for stochastic partial differential equations driven by Gaussian noise. I will introduce the relevant mathematical background from functional analysis, such as Hilbert-Schmidt and trace-class operators, and from the theory and infinite dimensional stochastic analysis, such as Gaussian measures on Hilbert spaces and stochastic integration in infinite dimensions. To focus on the main issues that arise in this theory, I will only consider equations with additive noise in Hilbert spaces but the concepts introduced can be generalized, with more technical effort, to equations with multiplicative noise and to Banach spaces. I will discuss the stochastic wave equation in more detail as a particular example. In part 2, I will describe a space-time approximation of the linear stochastic wave equation driven by additive nose. For the space-discretization I will introduce the relevant deterministic finite element theory, and for the time-discretization, the relevant theory for rational approximations of the exponential function. Both convergence in the mean-square sense and in the sense of weak convergence of probability measures will be discussed together with sketches of proofs.
(István Faragó, János Karátson, Róbert Horváth, Miklós Mincsovics)
Visit the homepage of the seminar: http://math.bme.hu/AlkAnalSzemi