references.bib

@article{gillespieMathematicsBrownianMotion1996,
  title = {The Mathematics of {{Brownian}} Motion and {{Johnson}} Noise},
  author = {Gillespie, Daniel T.},
  year = {1996},
  month = mar,
  journal = {American Journal of Physics},
  volume = {64},
  number = {3},
  pages = {225--240},
  issn = {0002-9505, 1943-2909},
  doi = {10.1119/1.18210},
  urldate = {2014-04-23},
  abstract = {One reason why Brownian motion and Johnson noise are difficult subjects to teach is that their mathematical requirements transcend the capabilities of ordinary differential calculus. Presented here is an exposition of the needed generalization of calculus, namely continuous Markov process theory, in a form that should be accessible to advanced physics undergraduates. It is shown how this mathematical framework enables one to give clear, concise derivations of all the principal results of Brownian motion and Johnson noise, including fluctuation{\textendash}dissipation formulas, auto-covariance transport formulas, spectral density formulas, Nyquist's formula, the notions of white and 1/f 2noise, and an accurate numerical simulation algorithm. An added benefit of this exposition is a clearer view of the mathematical connection between the two very different approaches to Brownian motion taken by Einstein and Langevin in their pioneering papers of 1905 and 1908.},
  keywords = {1/f noise,Brownian motion,Calculus,dynamical system,Fokker-Planck equation,Markov processes,primer,stochastic,Thermal noise},
  file = {/home/rene/var/Zotero/storage/PPKWD7XS/Gillespie - 1996 - The mathematics of Brownian motion and Johnson noi.pdf;/home/rene/var/Zotero/storage/TQB5NDW7/1.html}
}

@incollection{mateu-figuerasDistributionsSimplexRevisited2021,
  title = {Distributions on the {{Simplex Revisited}}},
  booktitle = {Advances in {{Compositional Data Analysis}}: {{Festschrift}} in {{Honour}} of {{Vera Pawlowsky-Glahn}}},
  author = {{Mateu-Figueras}, Gloria and Monti, Gianna S. and Egozcue, J. J.},
  editor = {Filzmoser, Peter and Hron, Karel and {Mart{\'i}n-Fern{\'a}ndez}, Josep Antoni and {Palarea-Albaladejo}, Javier},
  year = {2021},
  pages = {61--82},
  publisher = {{Springer International Publishing}},
  address = {{Cham}},
  doi = {10.1007/978-3-030-71175-7_4},
  urldate = {2022-12-26},
  abstract = {A large number of families of distributions are available to model multivariate real vectors. On the contrary, for the simplex sample space, we have only a limited number of families arising through the generalization of the Dirichlet family or the logratio normal family. This chapter tries to summarize those models and some generalizations with a special emphasis on the algebraic-geometric structure of the simplex and on the measure which is considered compatible. In particular, the shifted-scaled Dirichlet distribution is studied and the logratio t distribution is rewritten and studied with respect to the Aitchison measure.},
  isbn = {978-3-030-71175-7},
  langid = {english},
  file = {/home/rene/var/Zotero/storage/A6H585YL/Mateu-Figueras et al_2021_Distributions on the Simplex Revisited.pdf}
}

@unpublished{reneFalsifyingModels2024,
  title = {Falsifying models using empirical loss discrepancy},
  author = {René, Alexandre and Longtin, André},
  note = {In preparation}
}