arXiv 7 Oct 2019 · Mathematics — Probability
arXiv:1910.02577 · PDF · DOI · OpenAlex · Extracted main text
We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel data models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Billingsley, P (1968) Convergence of Probability Measures | 0.874 | 9 | 2 | 100% |
| 2 | Walsh, J. B (1986) Martingales with a multidimensional parameter and stochastic integrals in the plane | 0.511 | 2 | 1 | 100% |
| 3 | Berkes, I. and G. J. Morrow (1981) Strong invariance principles for mixing random fields | 0.405 | 1 | 1 | 100% |
| 4 | Bickel, P. J. and M. J. Wichura (1971) Convergence criteria for multiparameter stochastic processes and some applications | 0.405 | 1 | 1 | 100% |
| 5 | Volnỳ, D. and Y. Wang (2014) An invariance principle for stationary random fields under Hannan’s condition | 0.405 | 1 | 1 | 100% |
| 6 | Wang, Y. and M. Woodroofe (2013) A new condition for the invariance principle for stationary random fields | 0.405 | 1 | 1 | 100% |
Showing the top 6 of 6 scored citations.