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Matsuura Lab
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The lab uses analysis to study diffusion processes through symmetric Markov processes and Dirichlet forms.
AboutAbout the lab
Understanding diffusion processes through analysis
The Matsuura Lab studies analysis related to symmetric Markov processes, Dirichlet forms, and diffusion processes with boundary conditions.
It investigates reflecting Brownian motion on domains with boundary from a mathematical standpoint.
Another research topic is discrete approximation, in which reflecting Brownian motion is approached by Markov chains on partitions of the domain.
Key terms
- symmetric Markov process
- A random motion whose next move depends probabilistically only on its current state, and whose properties do not change when time is reversed
- Dirichlet form
- A mathematical form that represents the energy of a randomly moving object
- reflecting Brownian motion
- Brownian motion that moves randomly and is reflected back when it hits the boundary of a domain
- Markov chain
- A probabilistic sequence of transitions between states in which the next state depends only on the current state
ResearchResearch themes
The lab studies analysis related to diffusion processes with boundary conditions, based on symmetric Markov processes and Dirichlet forms. Its papers cover discrete approximation of reflecting Brownian motion, as well as time changes of Brownian motion and the Neumann Laplacian.
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MembersFaculty
- Assistant ProfessorKouhei Matsuura
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Random walk in1d” Flomenbom / CC BY-SA 3.0 (cropped)
- Reflecting Brownian Motion and Discrete Approximation: “Set Estimation from Reflected Brownian Motion 01” MGromov / CC BY-SA 4.0 (cropped)
- Related lab (Fukushima Lab): “Walk3d 2” No machine-readable author provided. Zweistein~commonswiki assumed (based on copyright claims). / CC BY 2.5 (cropped)
- Related lab (Hamana Lab): “Notions-of-convergence-in-probability-theory” Emptiless / Public domain (cropped)
- Related lab (Kakehi Lab): “Wave Interference” Cubitt Robert / CC BY-SA 4.0 (cropped)
- Related lab (Takeuchi Lab): “Soap Films” Ryan Somma / CC BY-SA 2.0 (cropped)
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