professor

Stochastic Analysis

uemura 
toshihiro

Professoruemura toshihiro

Field of Expertise

Stochastic Analysis

Stochastic processes are known as mathematical models for analyzing uncertain phenomena. I am, in particular, interesting in Markov processes, i.e., stochastic processes without memory; in real life, you will encounter such behavior, for example, in modeling stock prices.

If you keep rolling the (fair) dice, for example, the probability of getting a six comes as close to 1/6 as possible. Also,if you keep tossing (fair) coins, the probability of a coin coming up with a face is getting closer and closer to 1/2.
In this way, there are many phenomena in the world in which a certain situation will emerge if you continue to perform a certain operation. Let's use mathematics to analyze such phenomena.

Thesis Topics

  1. Hitting times of a random walk
  2. Mean visiting times of a Markov chain allowing short jumps
  3. Recurrence or transience of a Markov chain
  4. Partial differential operators and diffusion processes
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