## Introduction to Stochastic Calculus with Applications to Nonlinear Filtering - M4P67

### 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

## Introduction to Stochastic Calculus with Applications to Nonlinear Filtering - M5P67

### 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