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A Class of Non-Reversible Hypercube Long-Range Random Walks and Bernoulli Autoregression

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Abstract

We study a large class of long-range random walks which take values on the vertices of an N-dimensional hypercube. These processes are connected with multivariate Bernoulli autoregression.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.

References

  1. Collevecchio, A., Griffiths, R.C.: A class of random walks on the hypercube. In: Vares, M.E., Fernández, R., Fontes, L.R., Newman, C.M. (eds.) In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius Progress in Probability, vol. 77. Birkhäuser, Cham (2021)

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  2. Diaconis, P., Griffiths, R.C.: Exchangeable pairs of Bernoulli random variables, Krawtchouk polynomials, and Ehrenfest urns. Aust. N. Z. J. Stat. 54, 81–101 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Euán, C., Sun, Y.: Bernoulli vector autoregressive model. J. Multivar. Anal. 177, 105499 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fontana, R., Semeraro, P.: Representation of multivariate Bernoulli distributions with a given set of specified moments. J. Multivar. Anal. 168, 290–303 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  5. Teugels, J.F.: Some representations of the multivariate Bernoulli and Binomial distributions. J. Multivar. Anal. 32, 256–268 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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Funding

Andrea Collevecchio’s work is partially supported by Australian Research Council Grant DP180100613 and by Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) CE140100049.

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Melbourne, VIC, Australia

    Andrea Collevecchio & Robert Griffiths

Authors
  1. Andrea Collevecchio
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  2. Robert Griffiths
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Correspondence to Robert Griffiths.

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Collevecchio, A., Griffiths, R. A Class of Non-Reversible Hypercube Long-Range Random Walks and Bernoulli Autoregression. J Theor Probab 36, 623–645 (2023). https://doi.org/10.1007/s10959-022-01162-4

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  • DOI: https://doi.org/10.1007/s10959-022-01162-4

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