Imperial College London

ProfessorDanCrisan

Faculty of Natural SciencesDepartment of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

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)

6. Numerical Methods (the Extended Kalman-filter, Sequential Monte-Carlo methods).

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