Postgraduate study
Edinburgh: Extraordinary futures await.

Probability and Stochastics PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Probability and Stochastics

Our research group operates in what is perhaps the most widely applied area of mathematics. The financial sector, in particular, is a major focus of our research, and graduates with the right research experience can make their way into highly rewarding roles in industry.

As part of our small, specialised group, you'll enjoy a research environment that features a balance between theory and practice, access to one of the most powerful computing facilities in the UK and strong links with relevant industries.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Our research focuses on the following themes:

  • stochastic differential equations and stochastic partial differential equations (PDEs) and their applications in nonlinear filtering and stochastic control
  • applications of stochastic analysis of PDEs, stochastic PDEs and stochastic differential equations (accelerated numerical methods in particular)

We’re also involved in the applications of probability theory, mainly to mathematical finance, particularly stochastic volatility models, equivalent martingale measures and incomplete markets. Other applications include engineering, signal procession and biological sciences.

With the financial sector being the major commercial employer of our graduates, our involvement with the Scottish Financial Risk Academy, established in conjunction with Heriot-Watt University, offers valuable industry links and training.

You can benefit from short project internships with leading financial institutions, visits from leading risk scholars, and a series of knowledge exchange courses and events.

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

As part of the Probability & Stochastic Analysis group, you'll have access to the Edinburgh Parallel Computing Centre (EPCC), one of Europe’s leading supercomputing facilities. EPCC provides:

  • high-level grid computing
  • data integration
  • computer simulation
  • process optimisation

We offer training in all the relevant programs required to achieve your research aims.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

  • Maple
  • Matlab
  • Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

Many of our graduates take up lucrative positions with high-profile financial companies. A large number also pursue careers in academia, while others apply their skills in engineering or biological sciences.

These entry requirements are for the 2025/26 academic year and requirements for future academic years may differ. Entry requirements for the 2026/27 academic year will be published on 1 Oct 2025.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency which will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

  • IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
  • TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
  • C1 Advanced (CAE) / C2 Proficiency (CPE): total 176 with at least 169 in each component.
  • Trinity ISE: ISE II with distinctions in all four components.
  • PTE Academic: total 65 with at least 59 in each component. We do not accept PTE Academic Online.
  • Oxford ELLT: 7 overall with at least 6 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS, TOEFL, Trinity ISE or PTE, in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

If you are not a national of a majority English speaking country, then your degree must be no more than five years old at the beginning of your programme of study.

Find out more about our language requirements:

Tuition fees

Most PhD students in Mathematics receive full scholarships to cover their tuition fees and living costs.

Others may use a combination of the following funding to pay their tuition fees and living costs:

  • scholarships
  • borrowing money

    • taking out a loan
    • family support
  • personal savings
  • income from work
  • employer sponsorship

Explore sources of funding for postgraduate study

Featured funding

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

  • your programme
  • the duration of your studies
  • your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

Other funding opportunities

Search for scholarships and funding opportunities:

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 20 January 2025 will receive full consideration for funding. Later applications will be considered until all positions are filled.

Find out more about the general application process for postgraduate programmes:

Further information

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD