Rate of strong convergence to Markov-modulated Brownian motion
نویسندگان
چکیده
Abstract Latouche and Nguyen (2015b) constructed a sequence of stochastic fluid processes showed that it converges weakly to Markov-modulated Brownian motion (MMBM). Here, we construct different show strongly an MMBM. To the best our knowledge, this is first result on strong convergence motion. Besides implying weak convergence, such approximation constitutes powerful tool for developing deep results sophisticated models. Additionally, prove rate almost sure $o(n^{-1/2} \log n)$ . When reduced special case standard motion, improvement over obtained by in Gorostiza Griego (1980), which $o(n^{-1/2}(\log n)^{5/2})$
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2022
ISSN: ['1475-6072', '0021-9002']
DOI: https://doi.org/10.1017/jpr.2021.30