Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

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1 @book{Pazy1983,
2   author    = {Amnon Pazy},
3   title     = {Semigroups of Linear Operators and Applications to Partial Differential Equations},
4   series    = {Applied Mathematical Sciences},
5   volume    = {44},
6   publisher = {Springer},
7   address   = {New York},
8   year      = {1983}
9 }
10 
11 @book{EngelNagel2000,
12   author    = {Klaus Joachim Engel and Rainer Nagel},
13   title     = {One Parameter Semigroups for Linear Evolution Equations},
14   series    = {Graduate Texts in Mathematics},
15   volume    = {194},
16   publisher = {Springer},
17   address   = {New York},
18   year      = {2000}
19 }
20 
21 @book{KemenySnell1960,
22   author    = {John G. Kemeny and J. Laurie Snell},
23   title     = {Finite Markov Chains},
24   publisher = {D. Van Nostrand},
25   address   = {Princeton, New Jersey},
26   year      = {1960}
27 }
28 
29 @book{Norris1997,
30   author    = {J. R. Norris},
31   title     = {Markov Chains},
32   series    = {Cambridge Series in Statistical and Probabilistic Mathematics},
33   volume    = {2},
34   publisher = {Cambridge University Press},
35   address   = {Cambridge},
36   year      = {1997}
37 }
38 
39 @article{RogersPitman1981,
40   author  = {L. C. G. Rogers and J. W. Pitman},
41   title   = {Markov functions},
42   journal = {The Annals of Probability},
43   volume  = {9},
44   number  = {4},
45   pages   = {573{\textendash}582},
46   year    = {1981}
47 }
48 
49 @book{Williams1991,
50   author    = {David Williams},
51   title     = {Probability with Martingales},
52   publisher = {Cambridge University Press},
53   address   = {Cambridge},
54   year      = {1991}
55 }
56 
57 @book{BernardoSmith1994,
58   author    = {Jos\'{e} M. Bernardo and Adrian F. M. Smith},
59   title     = {Bayesian Theory},
60   publisher = {John Wiley and Sons},
61   address   = {Chichester},
62   year      = {1994}
63 }
64 
65 @article{Rabiner1989,
66   author  = {Lawrence R. Rabiner},
67   title   = {A tutorial on hidden Markov models and selected applications in speech recognition},
68   journal = {Proceedings of the IEEE},
69   volume  = {77},
70   number  = {2},
71   pages   = {257{\textendash}286},
72   year    = {1989}
73 }
74 
75 @article{Balakrishnan1960,
76   author  = {A. V. Balakrishnan},
77   title   = {Fractional powers of closed operators and the semigroups generated by them},
78   journal = {Pacific Journal of Mathematics},
79   volume  = {10},
80   number  = {2},
81   pages   = {419{\textendash}437},
82   year    = {1960}
83 }
84 
85 @book{SchillingSongVondracek2012,
86   author    = {Ren\'{e} L. Schilling and Renming Song and Zoran Vondra\v{c}ek},
87   title     = {Bernstein Functions},
88   edition   = {Second},
89   series    = {De Gruyter Studies in Mathematics},
90   volume    = {37},
91   publisher = {De Gruyter},
92   address   = {Berlin},
93   year      = {2012}
94 }
95 
96 @book{Strikwerda2004,
97   author    = {John C. Strikwerda},
98   title     = {Finite Difference Schemes and Partial Differential Equations},
99   edition   = {Second},
100   publisher = {Society for Industrial and Applied Mathematics},
101   address   = {Philadelphia},
102   year      = {2004}
103 }
104 
105 @article{Kac1949,
106   author  = {Mark Kac},
107   title   = {On distributions of certain Wiener functionals},
108   journal = {Transactions of the American Mathematical Society},
109   volume  = {65},
110   number  = {1},
111   pages   = {1{\textendash}13},
112   year    = {1949}
113 }
114 
115 @article{Feshbach1958,
116   author  = {Herman Feshbach},
117   title   = {Unified theory of nuclear reactions},
118   journal = {Annals of Physics},
119   volume  = {5},
120   number  = {4},
121   pages   = {357{\textendash}390},
122   year    = {1958}
123 }
124 
125 @article{Zwanzig1961,
126   author  = {Robert Zwanzig},
127   title   = {Memory effects in irreversible thermodynamics},
128   journal = {Physical Review},
129   volume  = {124},
130   number  = {4},
131   pages   = {983{\textendash}992},
132   year    = {1961}
133 }
134 
135 @article{ChorinHaldKupferman2000,
136   author  = {Alexandre J. Chorin and Ole H. Hald and Raz Kupferman},
137   title   = {Optimal prediction and the Mori Zwanzig representation of irreversible processes},
138   journal = {Proceedings of the National Academy of Sciences of the United States of America},
139   volume  = {97},
140   number  = {7},
141   pages   = {2968{\textendash}2973},
142   year    = {2000}
143 }
144 
145 @book{Kailath1980,
146   author    = {Thomas Kailath},
147   title     = {Linear Systems},
148   publisher = {Prentice Hall},
149   address   = {Englewood Cliffs, New Jersey},
150   year      = {1980}
151 }
152 
153 @book{Neuts1981,
154   author    = {Marcel F. Neuts},
155   title     = {Matrix Geometric Solutions in Stochastic Models},
156   publisher = {The Johns Hopkins University Press},
157   address   = {Baltimore},
158   year      = {1981}
159 }
160 
161 @article{AsmussenNermanOlsson1996,
162   author  = {S\o{}ren Asmussen and Olle Nerman and Marita Olsson},
163   title   = {Fitting phase type distributions via the expectation maximization algorithm},
164   journal = {Scandinavian Journal of Statistics},
165   volume  = {23},
166   number  = {4},
167   pages   = {419{\textendash}441},
168   year    = {1996}
169 }
170 
171 @book{Janson1997,
172   author    = {Svante Janson},
173   title     = {Gaussian Hilbert Spaces},
174   series    = {Cambridge Tracts in Mathematics},
175   volume    = {129},
176   publisher = {Cambridge University Press},
177   address   = {Cambridge},
178   year      = {1997}
179 }
180 
181 @book{CoverThomas2006,
182   author    = {Thomas M. Cover and Joy A. Thomas},
183   title     = {Elements of Information Theory},
184   edition   = {Second},
185   publisher = {John Wiley and Sons},
186   address   = {Hoboken, New Jersey},
187   year      = {2006}
188 }
189 
190 @book{DunfordSchwartz1958,
191   author    = {Nelson Dunford and Jacob T. Schwartz},
192   title     = {Linear Operators. Part I: General Theory},
193   series    = {Pure and Applied Mathematics},
194   volume    = {7},
195   publisher = {Interscience Publishers},
196   address   = {New York},
197   year      = {1958}
198 }
199 
200 @misc{TaylorBanachAlgebras,
201   author = {Michael E. Taylor},
202   title = {Lectures on {Banach} Algebras},
203   howpublished = {Author-hosted lecture notes},
204   note = {Undated; Appendix A. Accessed 6 October 2026},
205   url = {https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/banalg.pdf}
206 }

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