@book{Pazy1983,
  author    = {Amnon Pazy},
  title     = {Semigroups of Linear Operators and Applications to Partial Differential Equations},
  series    = {Applied Mathematical Sciences},
  volume    = {44},
  publisher = {Springer},
  address   = {New York},
  year      = {1983}
}

@book{EngelNagel2000,
  author    = {Klaus Joachim Engel and Rainer Nagel},
  title     = {One Parameter Semigroups for Linear Evolution Equations},
  series    = {Graduate Texts in Mathematics},
  volume    = {194},
  publisher = {Springer},
  address   = {New York},
  year      = {2000}
}

@book{KemenySnell1960,
  author    = {John G. Kemeny and J. Laurie Snell},
  title     = {Finite Markov Chains},
  publisher = {D. Van Nostrand},
  address   = {Princeton, New Jersey},
  year      = {1960}
}

@book{Norris1997,
  author    = {J. R. Norris},
  title     = {Markov Chains},
  series    = {Cambridge Series in Statistical and Probabilistic Mathematics},
  volume    = {2},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1997}
}

@article{RogersPitman1981,
  author  = {L. C. G. Rogers and J. W. Pitman},
  title   = {Markov functions},
  journal = {The Annals of Probability},
  volume  = {9},
  number  = {4},
  pages   = {573{\textendash}582},
  year    = {1981}
}

@book{Williams1991,
  author    = {David Williams},
  title     = {Probability with Martingales},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1991}
}

@book{BernardoSmith1994,
  author    = {Jos\'{e} M. Bernardo and Adrian F. M. Smith},
  title     = {Bayesian Theory},
  publisher = {John Wiley and Sons},
  address   = {Chichester},
  year      = {1994}
}

@article{Rabiner1989,
  author  = {Lawrence R. Rabiner},
  title   = {A tutorial on hidden Markov models and selected applications in speech recognition},
  journal = {Proceedings of the IEEE},
  volume  = {77},
  number  = {2},
  pages   = {257{\textendash}286},
  year    = {1989}
}

@article{Balakrishnan1960,
  author  = {A. V. Balakrishnan},
  title   = {Fractional powers of closed operators and the semigroups generated by them},
  journal = {Pacific Journal of Mathematics},
  volume  = {10},
  number  = {2},
  pages   = {419{\textendash}437},
  year    = {1960}
}

@book{SchillingSongVondracek2012,
  author    = {Ren\'{e} L. Schilling and Renming Song and Zoran Vondra\v{c}ek},
  title     = {Bernstein Functions},
  edition   = {Second},
  series    = {De Gruyter Studies in Mathematics},
  volume    = {37},
  publisher = {De Gruyter},
  address   = {Berlin},
  year      = {2012}
}

@book{Strikwerda2004,
  author    = {John C. Strikwerda},
  title     = {Finite Difference Schemes and Partial Differential Equations},
  edition   = {Second},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  year      = {2004}
}

@article{Kac1949,
  author  = {Mark Kac},
  title   = {On distributions of certain Wiener functionals},
  journal = {Transactions of the American Mathematical Society},
  volume  = {65},
  number  = {1},
  pages   = {1{\textendash}13},
  year    = {1949}
}

@article{Feshbach1958,
  author  = {Herman Feshbach},
  title   = {Unified theory of nuclear reactions},
  journal = {Annals of Physics},
  volume  = {5},
  number  = {4},
  pages   = {357{\textendash}390},
  year    = {1958}
}

@article{Zwanzig1961,
  author  = {Robert Zwanzig},
  title   = {Memory effects in irreversible thermodynamics},
  journal = {Physical Review},
  volume  = {124},
  number  = {4},
  pages   = {983{\textendash}992},
  year    = {1961}
}

@article{ChorinHaldKupferman2000,
  author  = {Alexandre J. Chorin and Ole H. Hald and Raz Kupferman},
  title   = {Optimal prediction and the Mori Zwanzig representation of irreversible processes},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  volume  = {97},
  number  = {7},
  pages   = {2968{\textendash}2973},
  year    = {2000}
}

@book{Kailath1980,
  author    = {Thomas Kailath},
  title     = {Linear Systems},
  publisher = {Prentice Hall},
  address   = {Englewood Cliffs, New Jersey},
  year      = {1980}
}

@book{Neuts1981,
  author    = {Marcel F. Neuts},
  title     = {Matrix Geometric Solutions in Stochastic Models},
  publisher = {The Johns Hopkins University Press},
  address   = {Baltimore},
  year      = {1981}
}

@article{AsmussenNermanOlsson1996,
  author  = {S\o{}ren Asmussen and Olle Nerman and Marita Olsson},
  title   = {Fitting phase type distributions via the expectation maximization algorithm},
  journal = {Scandinavian Journal of Statistics},
  volume  = {23},
  number  = {4},
  pages   = {419{\textendash}441},
  year    = {1996}
}

@book{Janson1997,
  author    = {Svante Janson},
  title     = {Gaussian Hilbert Spaces},
  series    = {Cambridge Tracts in Mathematics},
  volume    = {129},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1997}
}

@book{CoverThomas2006,
  author    = {Thomas M. Cover and Joy A. Thomas},
  title     = {Elements of Information Theory},
  edition   = {Second},
  publisher = {John Wiley and Sons},
  address   = {Hoboken, New Jersey},
  year      = {2006}
}

@book{DunfordSchwartz1958,
  author    = {Nelson Dunford and Jacob T. Schwartz},
  title     = {Linear Operators. Part I: General Theory},
  series    = {Pure and Applied Mathematics},
  volume    = {7},
  publisher = {Interscience Publishers},
  address   = {New York},
  year      = {1958}
}

@misc{TaylorBanachAlgebras,
  author = {Michael E. Taylor},
  title = {Lectures on {Banach} Algebras},
  howpublished = {Author-hosted lecture notes},
  note = {Undated; Appendix A. Accessed 6 October 2026},
  url = {https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/banalg.pdf}
}