Choose semester and course offering
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Content and learning outcomes
Course contents
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Conditional expectation, martingales and stochastic integrals in discrete time, stopping times, Girsanov Theorem.
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Martingales in continuous time, Brownian motion, Ito integral and Ito Lemma.
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Martingale representation Theorem, stochastic differential equations, Ito diffusions, Kolmogorov equations, Feynman-Kac formula, stopping times and optional stopping.
Intended learning outcomes
After passing the course, the students should be able to
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formulate and explain central definitions and theorems within the theory of martingales and stochastic integrals;
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solve basic problems within the theory of martingales and stochastic integrals, and apply its methods to stochastic processes.
Course Disposition
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Literature and preparations
Specific prerequisites
- Completed advanced course in probability theory (SF2940 or equivalent)
Recommended prerequisites
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Equipment
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Literature
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Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
A, B, C, D, E, FX, F
Examination
- TEN1 - Examination, 7,5 hp, betygsskala: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
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Opportunity to raise an approved grade via renewed examination
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Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course web
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.
Course web SF2971Offered by
Main field of study
Mathematics
Education cycle
Second cycle
Add-on studies
No information inserted
Contact
Thomas Önskog (onskog@kth.se)