Lévy Processes and Random Walks: a workshop in celebration of Ron Doney's 80th birthday
Lead Research Organisation:
University of Manchester
Department Name: Mathematics
Abstract
This is an application for partial funding for a 3-day research workshop in probability entitled Lévy processes and random walks: A workshop in celebration of Ron Doney's 80th birthday held at the University of Manchester, 21 July to 23 Julyl 2020.
A random walk is a discrete time stochastic process with independent increments. It is a fundamental model in Probability Theory and was studied in its early days as sums of independent random variables. The classical Law of Large Numbers and Central Limit Theorem form the base of Probability and Statistics. Lévy processes are a continuous time analogue of random walks. The most well-known examples of Lévy processes are Brownian motion and the Poisson process which appear throughout Probability Theory. Both random walks and Lévy processes have numerous applications not only in Probability but in other areas of mathematics, physics, biology and other sciences.
The workshop marks the 80th birthday of Professor Ron Doney, who is one of the world leading experts in this area. This occasion will bring twenty four invited talks from the leading experts in this area. The UK traditionally has a very strong representation in the area of Lévy processes and random walks and seven of these talks will be given by UK-based academics. Our workshop focuses on the new developments in this area and applications to other of research including mathematical biology and risk, finance and insurance. Alongside the talks there will be opportunities for PhD students and early career researchers to present their work at a poster session.
The meeting will benefit UK mathematics by enhancing interactions between UK and international experts on recent developments and future directions in random walks and Lévy processes. Particular emphasis is placed on the participation of female academics and early career researchers.
A random walk is a discrete time stochastic process with independent increments. It is a fundamental model in Probability Theory and was studied in its early days as sums of independent random variables. The classical Law of Large Numbers and Central Limit Theorem form the base of Probability and Statistics. Lévy processes are a continuous time analogue of random walks. The most well-known examples of Lévy processes are Brownian motion and the Poisson process which appear throughout Probability Theory. Both random walks and Lévy processes have numerous applications not only in Probability but in other areas of mathematics, physics, biology and other sciences.
The workshop marks the 80th birthday of Professor Ron Doney, who is one of the world leading experts in this area. This occasion will bring twenty four invited talks from the leading experts in this area. The UK traditionally has a very strong representation in the area of Lévy processes and random walks and seven of these talks will be given by UK-based academics. Our workshop focuses on the new developments in this area and applications to other of research including mathematical biology and risk, finance and insurance. Alongside the talks there will be opportunities for PhD students and early career researchers to present their work at a poster session.
The meeting will benefit UK mathematics by enhancing interactions between UK and international experts on recent developments and future directions in random walks and Lévy processes. Particular emphasis is placed on the participation of female academics and early career researchers.
Planned Impact
The impacts of a conference such as this are numerous and diverse, extending far beyond its duration. The workshop will
bring together the UK community in Levy processes and random walks with internationally renowned researchers, and and provide opportunities for new collaborations and discussions to develop.
The attendees will learn about new techniques and recent development in this quickly developing area from internationally-renowned invited lecturers, and will make new
contacts and strengthen existing ones, which will lead to future impactful research. As such, a major impact of the
workshop is to strengthen the UK research base in this area and due to the fundamental role played by random walks and Levy processes in more general area if Probability.
Our choice of topics have close links to mathematical physics, stochastic modelling, finance and risk theory, theoretical population genetics and mathematical ecology.
This will invigorate the UK research community, and result in impactful research being carried out in Levy procesess and random walks, and more generally in Probability and its numerous application areas over the
coming years.
We will pay particular emphasis on the development of PhD students and other early career researchers in probability, a
group of researchers with strong potential to produce impactful research in the future. This group of researchers will have
the opportunity to present their work at the poster session, and will have opportunities to interact with leading world experts in the area.
To maximise the potential impact of the workshop, we will advertise widely through national mailing lists on probability and
the applications areas in physics and biology and related fields, and networks of contacts at UK universities. We will also
advertise to companies with an interest in the above and related research areas.
bring together the UK community in Levy processes and random walks with internationally renowned researchers, and and provide opportunities for new collaborations and discussions to develop.
The attendees will learn about new techniques and recent development in this quickly developing area from internationally-renowned invited lecturers, and will make new
contacts and strengthen existing ones, which will lead to future impactful research. As such, a major impact of the
workshop is to strengthen the UK research base in this area and due to the fundamental role played by random walks and Levy processes in more general area if Probability.
Our choice of topics have close links to mathematical physics, stochastic modelling, finance and risk theory, theoretical population genetics and mathematical ecology.
This will invigorate the UK research community, and result in impactful research being carried out in Levy procesess and random walks, and more generally in Probability and its numerous application areas over the
coming years.
We will pay particular emphasis on the development of PhD students and other early career researchers in probability, a
group of researchers with strong potential to produce impactful research in the future. This group of researchers will have
the opportunity to present their work at the poster session, and will have opportunities to interact with leading world experts in the area.
To maximise the potential impact of the workshop, we will advertise widely through national mailing lists on probability and
the applications areas in physics and biology and related fields, and networks of contacts at UK universities. We will also
advertise to companies with an interest in the above and related research areas.
Organisations
| Description | We held a meeting discussing the recent advances in the area of Lévy processes and random walks. This meeting allowed us to achieve the original aims of the workshop, which are 1. Dissemination of recent advances in Lévy processes, random walks and their applications, especially those with connections to biology, risk, finance and insurance. 2. Bringing together experts from the UK and the international community in this area and more generally Probability, as well as research students and early career researchers. 3. Identifying future research directions and promoting new opportunities for collaboration. 4. Training researchers in early stages of their career, in particular PhD students; thus contributing to the development of the next generation of UK-based mathematicians. PhD students were able to present posters about their research to a wider audience and learn from the international experts in the area of Probability. |
| Exploitation Route | The workshop will give an opportunity for these academics to present their work to a wider international community. The speakers and other participants benefitted from interaction between themselves and international experts in this and related areas. The PhD students and early career researchers presented their posters, making their work available to a wide international community in this area. This meeting will benefit UK probability and mathematics by providing an opportunity for the UK probability and international researchers to learn about the latest advances in this fundamental area of Probability, and form new collaborations and strengthen existing ones. |
| Sectors | Education |
| URL | https://personalpages.manchester.ac.uk/staff/denis.denisov/LevyRW-workshop/index.html |
| Description | Web site about the workshop |
| Form Of Engagement Activity | Engagement focused website, blog or social media channel |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | We have created a web site which contains up-to-date information about the workshop. |
| Year(s) Of Engagement Activity | 2020,2021,2022 |
| URL | https://personalpages.manchester.ac.uk/staff/denis.denisov/LevyRW-workshop/index.html |