Bounds simulation for fluid flow model of the second order
DOI:
https://doi.org/10.17721/1812-5409.2026/1.6Keywords:
strong simulation, acceptance-rejection sampling with squeezing, quantile transformationAbstract
This paper presents an approximation formula for the conditional cumulative distribution function of the maximum of a Brownian bridge with a given minimum. The formula enables us to develop an algorithm that generates the minimum and the upper bound of the maximum for a Brownian bridge trajectory. Thus, we can determine the simulation procedure for the upper and lower limits of a second-order fluid flow model. The demonstration of the results of the algorithm for a specific set of parameters is given. The extrema empirical distributions obtained using the sequential discretisation method and the approximate quantile method are compared. The possibility of sampling points in the middle of intervals, as well as choosing one of the subintervals at which the minimum is achieved, is considered.
Pages of the article in the issue: 43 - 54
Language of the article: English
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