Theory of Stochastic Processes
Teorin för stokastiska processer

FMS015F, 7.5 högskolepoäng

Gäller från och med: Spring 2014
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-04-22

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

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.

Mål

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.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, seminarier, övningar

Kursens examination

Examinationsform: Muntlig tentamen. Tatyana Turova
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: 60 hp in Mathematics
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.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvarig: Tatyana Turova <tatyana.turova@matstat.lu.se>