Abstract
The paper considers random processes with values in a vector Skorokhod space; i.e., in a product of a finite number of Skorokhod spaces. Our interest is focused on weak convergence of a sequence of such processes. Particularly, we present a criterion for weak convergence in vector Skorokhod spaces. The idea is based on an embedding of a vector Skorokhod space into a Skorokhod space. Also, an illustrative example of two empirical processes is attached.
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Acknowledgements
The author is thankful to anonymous referee for his comments and suggestions helping to improve the text.
The research was supported by the Czech Science Foundation (GA ČR) under the project 18-05631S.
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Lachout, P. (2019). A Criterion for Weak Convergence in Vector Skorokhod Spaces. In: Steland, A., Rafajłowicz, E., Okhrin, O. (eds) Stochastic Models, Statistics and Their Applications. SMSA 2019. Springer Proceedings in Mathematics & Statistics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-030-28665-1_7
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DOI: https://doi.org/10.1007/978-3-030-28665-1_7
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