Stochastic Calculus with Applications to non-Linear Filtering - MATH97061
Aims
The course will have six sections:
1. Martingales on Continuous Time (Doob Meyer decomposition, L_p bounds, Brownian motion, exponential martingales, semi-martingales, local martingales, Novikov’s condition)
2. Stochastic Calculus (Ito’s isometry, chain rule, integration by parts)
3. Stochastic Differential Equations (well posedness, linear SDEs, the Ornstein-Uhlenbeck process, Girsanov's Theorem)
4. Stochastic Filtering (definition, mathematical model for the signal process and the observation process)
5. The Filtering Equations (well-posedness, the innovation process, the Kalman-Bucy filter)
Role
Lecturer
Stochastic Calculus with Applications to non-Linear Filtering - MATH97172
Aims
The course will have six sections:
1. Martingales on Continuous Time (Doob Meyer decomposition, L_p bounds, Brownian motion, exponential martingales, semi-martingales, local martingales, Novikov’s condition)
2. Stochastic Calculus (Ito’s isometry, chain rule, integration by parts)
3. Stochastic Differential Equations (well posedness, linear SDEs, the Ornstein-Uhlenbeck process, Girsanov's Theorem)
4. Stochastic Filtering (definition, mathematical model for the signal process and the observation process)
5. The Filtering Equations (well-posedness, the innovation process, the Kalman-Bucy filter)
6. Numerical Methods (the Extended Kalman-filter, Sequential Monte-Carlo methods).
Role
Lecturer