Mathematisches Kolloquium
Am Donnerstag, 19. November 2020, um 16:30 Uhr spricht
Prof. Dr. Lukas Gonon
(LMU
)
im Hörsaal A027.
The lecture hall A027 provides 23 seats (LMU's infection control measures are in place).
A simultaneous online-broadcast of the talk is provided via the following link: Topic: Mathematisches Kolloquium
Join Zoom Meeting: https://lmu-munich.zoom.us/j/99946902916?pwd=UWM5SGtIL091NmdjU3BHVVpOU0lEdz09
Meeting ID: 999 4690 2916
Passcode: 695211
über das Thema
Dynamic learning for stochastic processes: neural networks, reservoir computing systems and applications to mathematical finance (Vorstellung zur Habilitation)
Zusammenfassung: In this talk we discuss recent mathematical results regarding different dynamic learning techniques for stochastic processes. We start with deep neural network expression rates for option prices for certain stochastic processes with jumps and the associated partial integro-differential equations. Subsequently, we study approximation and learning based on random recurrent neural networks and more general reservoir computing systems. We obtain high-probability bounds on the approximation error in terms of the network parameters and generalization error bounds for weakly dependent input data. Finally, we elaborate on various further research directions.