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Tightness for processes with fixed points of discontinuities and applications in varying environment. (English) Zbl 1352.60005

Electron. Commun. Probab. 21, Paper No. 81, 9 p. (2016).

Summary: We establish a sufficient condition for the tightness of a sequence of stochastic processes. Our condition makes it possible to study processes with accumulations of fixed times of discontinuity. Our motivation comes from the study of processes in varying or random environment. We demonstrate the usefulness of our condition on two examples: Galton Watson branching processes in varying environment and logistic branching processes with catastrophes.

Cited in 3 Documents

MSC:

60B10

Convergence of probability measures

Keywords:

tightness; fixed points of discontinuity; varying environment

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