大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,The University of Osaka

Quasi-stationary distributions for standard processes with no negative jumps

山戸 康祐 (大阪大学)

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4. Quasi-stationary distributions for standard processes with no negative jumps

UQ-Osaka Seminar on Financial Mathematics and Economics 第６回 (University of QueenslandとMMDS金融保険部門共催)

Quasi-stationary distributions for standard processes with no negative jumps

山戸 康祐 (大阪大学)

Markov processes with killing arise naturally in various stochastic models, such as the surplus process of an insurance company, population models in mathematical biology, and metastable states in nonequilibrium statistical mechanics. For such processes, a quasi-stationary distribution (QSD) serves as a conditional version of the stationary distribution, and the existence of a QSD and convergence to it, known as the Yaglom limit, play a fundamental role in understanding the stability of the system and the long-term extinction rate.