In this talk, I will review the previous studies on quasi-stationary distributions for Markov processes. I will summarize the class of stochastic processes and typical methods that have been studied so far. In particular, I will focus on birth-and-death processes and one-dimensional diffusions, which have been studied extensively due to their simplicity. If time permits, I will overview my study on the domain of attraction of non-minimal quasi-stationary distributions of one-dimensional diffusions.

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In Student Colloquium, we do not fix the end time. Though a nominal time is shown above, we mean neither that it will be so, nor that it was so.