Stochastic Processes and Simulation II
This course covers mainly Renewal theory, where we by removing the assumption that stochastic processes are memoryless consider models that are more complicated but more realistic than in previous courses, and Brownian motion, the random movement of a particles in a medium.
The course covers renewal theory, methods of stochastic simulation and the theory of Brownian motion.
Renewal Theory: A basic assumptions during previous courses is that stochastic processes are memoryless (Markovian). In the renewal theory we drop this assumption and study processes where the future advancement is not linked to the past. Therefore we lose some simplicity and elegance, but instead we obtain significantly more realistic results.
Brownian Motion: When a particle moves randomly, (like, for instance, a molecule in gas), its movement can often be viewed upon as a sum of a large number of impulses (collisions with other molecules in the gas). Due to the fact that the sums of stochastic variables are normally distributed, the particle's movements should approximately be normally distributed. Assuming that the time perspective of interest is a lot larger then the interval between two impulses, it follows that the particle's location is normally distributed. Then the particle describes Brownian motion. This mathematical model is frequently used, not only within physics, but also in many other areas of science and economy.
Information for admitted students spring 2025
Congratulations! You have been admitted at Stockholm University and we hope that you will enjoy your studies with us.
In order to ensure that your studies begin as smoothly as possible we have compiled a short checklist for the beginning of the semester.
Follow the instructions on whether you have to reply to your offer or not.
universityadmissions.se
Checklist for admitted students
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Activate your university account
The first step in being able to register and gain access to all the university's IT services.
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Register at your department
Registration can be done in different ways. Read the instructions from your department below.
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Read all the information on this page
Here you will find what you need to know before your course or programme starts.
IMPORTANT
Your seat may be withdrawn if you do not register according to the instructions provided by your department.
Information from the department - courses
Here you can find information about online registration times, our learning platform, and what it means if you are conditionally admitted or placed on a reserve list.
First: Reply to your offer!
If you are offered a place or reserve place in the first notification of selection results, you must reply to it via Universityadmissions.se by 16 December to keep your place! If you have forgotten to do so you may be able to reaplpy via Universityadmissions.se (you can only do so if late application is open).
Info at Universityadmissions.se about replying to your offer
Registration in Ladok
Once you are admitted to a course you must register online via student.ladok.se to keep your place. Online registration opens 7 January, and closes at different times for different courses.
- Mathematics I (only given in Swedish): last day for registration is 15 January.
- Courses given and/or examined at KTH, so courses with the following course codes: BE7012, MM7051: last day for registration is 20 January. Register earlier if you can to get your KTH-account earlier.
- Other courses starting in January: last day for registration is 9 February.
- Other courses starting in March: last day for registration is 13 April.
You cannot register online for degree project courses in mathematics, we will register you for these when your project plan has been approved.
Learning platform
Our course pages can be found at kurser.math.su.se.
On most of the course pages you can "self enrol", but doing this does not mean that you are registered for the course! It only gives you access to the course page. You always have to register in Ladok separately, see above about registration.
Conditionally admitted
It is quite common that a student at the time of application has not finished all courses that are given as special eligibility requirements for the course or programme the student has applied for. This will result in the admission status "Conditionally admitted".
We will go through the conditions just before the courses start. As long as the condition remains you cannot register for the course in Ladok. If the condition is still in place by the time the course starts, and you haven't received any notification about whether or not you'll be allowed to take the course or programme you have applied for, contact our study advisors. If the course is one where online registration closes early, contact us before it closes.
You can also be conditionally admitted because you need to pay a tuition fee. You can find more information on tuition fees here:
Payment and repayment of tuition fee
Placed on reserve list
If you have a reserve place for a course, we may be able to offer you a spot in which case we will contact you around the start of the semester. If you have a conditional reserve place and are offered a place on the course, you also need to fulfil the condition(s) before you can take your place on the course.
More information
New student: information about admission, registration, course literature and course web
Welcome activities
Stockholm University organises a series of welcome activities that stretch over a few weeks at the beginning of each semester. The programme is voluntary (attendance is optional) and includes Arrival Service at the airport and an Orientation Day, see more details about these events below.
Your department may also organise activities for welcoming international students. More information will be provided by your specific department.
Find your way on campus
Stockholm University's main campus is in the Frescati area, north of the city centre. While most of our departments and offices are located here, there are also campus areas in other parts of the city.
Read more
For new international students
The course covers renewal theory, methods of stochastic simulation and the theory of Brownian motion.
Renewal Theory: A basic assumptions during previous courses is that stochastic processes are memoryless (Markovian). In the renewal theory we drop this assumption and study processes where the future advancement is not linked to the past. Therefore we lose some simplicity and elegance, but instead we obtain significantly more realistic results.
Brownian Motion: When a particle moves randomly, (like, for instance, a molecule in gas), its movement can often be viewed upon as a sum of a large number of impulses (collisions with other molecules in the gas). Due to the fact that the sums of stochastic variables are normally distributed, the particle's movements should approximately be normally distributed. Assuming that the time perspective of interest is a lot larger then the interval between two impulses, it follows that the particle's location is normally distributed. Then the particle describes Brownian motion. This mathematical model is frequently used, not only within physics, but also in many other areas of science and economy.
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Course structure
The course consists of two elements, theory and computer exercises.
Teaching format
Instruction is given in the form of lectures, exercise sessions and computer exercises.
Assessment
Examination for the course is done with a written examination, and written presentation of the computer exercises.
Examiner
A list of examiners can be found on
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Schedule
The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course. -
Course literature
Note that the course literature can be changed up to two months before the start of the course.
Ross: Introduction to probability models. Academic Press.
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Course reports
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More information
New student
During your studiesCourse web
We do not use Athena, you can find our course webpages on kurser.math.su.se.
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Contact
