Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22
Division: Mathematical Statistics
Course type: Third-cycle course
Teaching language: English
The course is a natural continuation of the study of probability theory as a part of mathematical education in Lund University. The aim of the course is to provide introduction into the theory of stochastic processes. The course gives necessary insight into the theory of stochastic processes for PhD students in other areas that use stochastic processes in their research. The course is the basic part for further studies in the theory of stochastic processes and stochastic differential equation. With respect to the theory there is no overlap of this course with any other course given at the Mathematical center.
Knowledge and Understanding
For a passing grade the doctoral student must
Stochastic integrals of deterministic functions. Shift operators Correlation functions. Spectral representation. Infinite-dimensional distributions. Kolmogorov Theorem on ex- tension. Markov moments, martingales. Markov processes, Markov properties and related operators. Trajectories of Markov processes with continuous time. Infinitesimal operators. Diffusion processes. Stochastic differential. Ito’s formula.
Wentzell, A.D.: A Course in the Theory of Stochastic Processes.
Also Brownian Motion and Stochastic Calculus” av I. Karatzas and S. Shreve, ”Probability” av A.N. Shiryaev, ”Foundations of Modern Probability” av O. Kallenberg
Types of instruction: Lectures, seminars, exercises
Examination format: Oral exam.
Grading scale: Failed, pass
Admission requirements: 60 hp in Mathematics
Assumed prior knowledge: The students are expected to know at least some measure theory and probability theory
Selection criteria: The course is part of the main field of studies in Mathematical Statistics at the Faculty of Science. The course is optional at the Second cycle in a Masters degree in Mathematics or Statistics, or even for the doctoral studies. The course is also offered as a single subject course.
Course coordinator: Tatyana Turova <firstname.lastname@example.org>