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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for Course FMS015F Theory of Stochastic Processes

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General
  • FMS015F
  • Temporary
Course Name
  • Theory of Stochastic Processes
Course Extent
  • 7.5
Type of Instruction
  • Third-cycle course
Administrative Information
  • 7152 (Centre of Mathematical Sciences / Mathematical Statistics)
  •  -04-22
  • FN1/Anders Gustafsson

Current Established Course Syllabus

General
  • English
  • If sufficient demand
  • Apply through e-mail
Aim
  • 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.
Contents
  • 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.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • have developed the ability for mathematical communication orally and in writing
    be familiar with basic concepts and methods in stochastic processes
    have acquired basic knowledge for further studies in mathematics and probability in particular.
Competences and Skills
  • For a passing grade the doctoral student must
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Seminars
  • Exercises
Examination Formats
  • Oral exam
  • Tatyana Turova
  • 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.
Literature
  • 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
Further Information
Course code
  • FMS015F
Administrative Information
  •  -04-22
  • FN1/Anders Gustafsson

All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2014 2014‑03‑31 11:37:44 2014‑03‑31 11:46:36 2014‑04‑22

Current or Upcoming Published Course Occasion

No matching course occasion was found.

All Published Course Occasions

1 course occasion.

Course syllabus valid from Start Date End Date Published
Spring 2014 2018‑02‑01 2018‑06‑01 2018‑01‑24

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