Strong Gaussian approximation for cumulative processes

2020/06/17 by Elena Bashtova, Bashtova, Elena, A. P. Shashkin +1
Decision Sciences · Economics, Econometrics and Finance · #60F17 (Primary) 60K25 (Secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2006.09583

openalex publication_date 2020/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Komlós-Major-Tusnády type are obtained. Provided examples include applications to stopped sums and birth and death processes.

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