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HU Credits:
4
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Ohad Noy Feldheim
Coordinator Office Hours:
By appointment
Teaching Staff:
Prof Feldheim Ohad
Course/Module description:
A second course in probability theory, from the standpoint of measure theory. The course revolves around stochastic processes, their invariants and convergence. These topics are studies via classical tools such as characteristic function, and modern tools such as martingales.
Course/Module aims:
Same as in learning outcomes.
Learning outcomes - On successful completion of this module, students should be able to:
Establishing probability theory on the shoulders of measure thoery.
Ability to prove the fundamental theorems in that theory in a general form.
Relating probability theory and harmonic analysis via characteristic functions.
Understanding discrete stochastic processes through the notion of a martingale.
familiarity with the wiener process (Brownian motion), and deriving its basic properties from simple random walks.
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lecture
Course/Module Content:
Convergence of random variables
Law of large numbers
Characteristic functions
Central limit theorem
Martingales
Other or different topic may be taught
Required Reading:
Lecture notes
Additional Reading Material:
Hebrew Notes
Probability with martinagles / Williams
Probability: Theory and Examples Rick Durrett
Grading Scheme :
Written / Oral / Practical Exam 100 %
Additional information:
none
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