In the Netherlands, PhD students (promovendi) are formally considered academic researchers rather than students.
If you are independently funded (research time made available by your employer, your own funds, student loan, grant from your home country etc.), you can apply directly to the "Graduate Programme in Mathematics and Statistics" to become a PhD student. For this, you use the KdVI-PhD Application Form at the bottom of this page.
Typically, young mathematicians (recent MSc), working at an institute of higher education, who wish to pursue a PhD at the KdV Institute. However, the programme is in principle open to mathematicians with an MSc degree.
Candidates do their PhD studies and preparatory work mostly at their home institution. They will visit the KdVI for a period of two to three months per year to consult with their advisor. KdVI will in general not be able to provide funding for these visits. It is possible, and it is encouraged by KdVI, that part of the daily guidance is done by qualified members of the home institution.
You need a Dutch Masters degree in mathematics or stochastics, or a degree in an adjacent field with sufficient mathematics. Foreign degrees which are equivalent to such a Dutch master degree also give access to the PhD Programme. The Doctorate Board of the University decides whether a foreign degree is equivalent to a Dutch one.
The tuition fee is € 1000 euro per year. Students will get a guest status at the KdVI, which includes electronic library facilities. During their visits to KdVI they will have a desk, library and computer facilities. Note that PhD students do not have student status in the Netherlands! In special cases the department may waive the fee.
Each accepted student will be assigned an academic mentor. The mentor will give the student instructions about the work and studies he/she should do in the first year. The mentor will also play a crucial role in the evaluation. In consultation with the student, the mentor will look for a PhD-supervisor. The mentor is not to be confused with a PhD thesis supervisor (even though the mentor can become the PhD thesis supervisor).
After the first year, the PhD student will be evaluated by the mentor and the director of KdVI. The evaluation is based on the general performance of the student. A student can only be positively evaluated if he or she has found a PhD thesis supervisor or topic. Positively evaluated PhD students are accepted for three more years.
After the evaluation, the main emphasis is on the independent research in the PhD thesis project. To get an impression of possible PhD thesis topics, you can look in UvA Dare. See the link below.