Detaljer för kurs FMS015F Theory of Stochastic Processes

Aktuell fastställd kursplan

Allmänt

Syfte

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.

Innehåll

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.

Kunskap och förståelse

För godkänd kurs skall doktoranden
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.

Färdighet och förmåga

Värderingsförmåga och förhållningssätt

Undervisningsformer

Examinationsformer

Förkunskapskrav

Förutsatta förkunskaper

The students are expected to know at least some measure theory and probability theory

Urvalskriterier

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.

Litteratur

Litteratur:
Wentzell, A.D.: A Course in the Theory of Stochastic Processes.
Kommentarer:
Also Brownian Motion and Stochastic Calculus” av I. Karatzas and S. Shreve,
”Probability” av A.N. Shiryaev,

”Foundations of Modern Probability” av O. Kallenberg

Övrig information

Kurskod

Administrativ information

1 kursplan.

Gäller från och med	Första inlämning	Andra inlämning	Fastställd
Spring 2014	2014‑03‑31 11:37:44	2014‑03‑31 11:46:36	2014‑04‑22

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1 kurstillfälle.

Kursplan giltig från	Startdatum	Slutdatum	Publicerad
Spring 2014	2018‑02‑01	2018‑06‑01	2018‑01‑24