# 401-3642-00L Brownian Motion and Stochastic Calculus

Semester | Spring Semester 2012 |

Lecturers | M. Schweizer |

Periodicity | yearly course |

Language of instruction | English |

Abstract | This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed: - Brownian motion - Markov processes - Stochastic calculus - Levy processes |

Objective | This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed: - Brownian motion: definition, construction, some important properties - Markov processes: basics, strong Markov property, generators and martingale problems - Stochastic calculus: semimartingales, stochastic integrals, Ito formula, Girsanov transformation, stochastic differential equations - Levy processes: basic notions, some important properties |

Content | This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed: - Brownian motion: definition, construction, some important properties - Markov processes: basics, strong Markov property, generators and martingale problems - Stochastic calculus: semimartingales, stochastic integrals, Ito formula, Girsanov transformation, stochastic differential equations - Levy processes: basic notions, some important properties |

Lecture notes | will be available for purchase |

Literature | Durrett, R., "Stochastic Calculus. A Practical Introduction", CRC Press, 1996. Ikeda, N. and Watanabe, S., "Stochastic Differential Equations and Diffusion Processes", second edition, North Holland, Amsterdam, 1979. Karatzas, I. and Shreve, S., "Brownian Motion and Stochastic Calculus", second edition, Springer, Berlin, 1991. Revuz, D. and Yor, M., "Continuous Martingales and Brownian Motion", second edition, Springer, Berlin, 1994. Rogers, L.C.G. and Williams, D., "Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Wiley, Chichester, 2000, 1994. Sato, K., "Levy Processes and Infinitely Divisible Distributions", Cambridge University Press, 1999. |

Prerequisites / Notice | This course replaces the former course 401-3642-00L Stochastic Processes and Stochastic Analysis. Moreover it has a large overlap with the course 401-4608-10L Brownian Motion and Stochastic Calculus from FS 2010. Therefore it is forbidden to register for an examination for more than one of the three courses mentioned. |