seminar: Ornstein-Uhlenbeck Bridge and Applications to Semilinear SPDE's
speaker: Bohdan Maslowski (Mathematical Institute, Czech Academy of Sciences)abstract: By the Ornstein-Uhlenbeck Bridge we understand a solution to linear stochastic equation with a given initial condition that is conditioned to go to a given point in the state space at terminal time. Definition of the OU Bridge is given and basic properties in infinite dimensions are studied. A formula for the transition density of the Markov semigroup defined by a semilinear stochastic equation is given by means of the OU Bridge and some useful properties are derived: Regularity of transition densities, Hilbert-Schmidt property and a hyperboundedness type result are proved. Furthermore, this approach may be used to obtain uniform estimates on constants in the definitions of V-uniform ergodicity and uniform exponential ergodicity. In the second part of the talk, these results are used to solve the stochastic ergodic and adaptive control problem in infinite dimensions (based on joint papers with Ben Goldys).
timetable:
Thu 6 Apr, 11:50 - 12:30, Aula Dini
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