---
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      given: David
  citation-key: ApplebaumLevy2004
  container-title: Notices of the AMS
  issue: '11'
  issued:
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  page: 1336-1347
  title: Lévy processes — from probability to finance and quantum groups
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- id: ApplebaumLevy2009
  author:
    - family: Applebaum
      given: David
  call-number: QA274.73 .A67 2009
  citation-key: ApplebaumLevy2009
  collection-number: '116'
  collection-title: Cambridge studies in advanced mathematics
  edition: 2nd ed
  event-place: Cambridge ; New York
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  number-of-pages: '460'
  publisher: Cambridge University Press
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  title: Lévy processes and stochastic calculus
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- id: ArrasStein2019
  accessed:
    - year: 2021
      month: 6
      day: 4
  author:
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      given: Benjamin
    - family: Houdré
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  citation-key: ArrasStein2019
  collection-title: SpringerBriefs in Probability and Mathematical Statistics
  DOI: 10.1007/978-3-030-15017-4_1
  editor:
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  event-place: Cham
  ISBN: 978-3-030-15017-4
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    - year: 2019
  language: en
  publisher: Springer International Publishing
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  title: On Stein's Method for Infinitely Divisible Laws with Finite First Moment
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- id: AsmussenStochastic2007
  author:
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      given: Søren
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  edition: 2007 edition
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      day: 27
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- id: AurzadaSmall2009
  accessed:
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  container-title: The Annals of Probability
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  DOI: 10.1214/09-AOP457
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  language: en
  page: 2066-2092
  title: Small deviations of general Lévy processes
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- id: AvramidisNew2003
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  citation-key: AvramidisNew2003
  collection-title: WSC '03
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    New Simulation Methodology for Finance: Efficient Simulation of Gamma and
    Variance-gamma Processes
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- id: BarndorffNielsenBasics2012
  author:
    - family: Barndorff-Nielsen
      given: Ole E
    - family: Shephard
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  citation-key: BarndorffNielsenBasics2012
  container-title: Lévy Driven Volatility Models
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  language: en
  page: '70'
  title: Basics of Lévy processes
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    https://pdfs.semanticscholar.org/fe80/07ba98fafa23ddca98ac5d9b1cf1732f70bd.pdf

- id: BarndorffNielsenMultivariate2001
  author:
    - family: Barndorff-Nielsen
      given: Ole E.
    - family: Pedersen
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    - family: Sato
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  citation-key: BarndorffNielsenMultivariate2001
  container-title: Advances in Applied Probability
  DOI: 10.1017/S0001867800010685
  ISSN: 0001-8678, 1475-6064
  issue: '1'
  issued:
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      month: 3
  page: 160-187
  title: Multivariate subordination, self-decomposability and stability
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  volume: '33'

- id: BarndorffNielsenMultivariate2011
  accessed:
    - year: 2019
      month: 10
      day: 9
  author:
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    - family: Stelzer
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  citation-key: BarndorffNielsenMultivariate2011
  container-title: The Annals of Applied Probability
  container-title-short: Ann. Appl. Probab.
  DOI: 10.1214/10-AAP690
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  language: EN
  page: 140-182
  publisher: Institute of Mathematical Statistics
  title: Multivariate supOU processes
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  volume: '21'

- id: BelomestnyStatistical2011
  accessed:
    - year: 2020
      month: 1
      day: 21
  author:
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      given: Denis
  citation-key: BelomestnyStatistical2011
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/11-AOS901
  ISSN: 0090-5364
  issue: '4'
  issued:
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  language: en
  page: 2205-2242
  title: >-
    Statistical inference for time-changed Lévy processes via composite
    characteristic function estimation
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  URL: http://arxiv.org/abs/1003.0275
  volume: '39'

- id: BertoinLevy1996
  author:
    - family: Bertoin
      given: Jean
  call-number: QA274.73 .B48 1996
  citation-key: BertoinLevy1996
  collection-number: '121'
  collection-title: Cambridge tracts in mathematics
  event-place: Cambridge ; New York
  ISBN: 978-0-521-56243-0
  issued:
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  number-of-pages: '265'
  publisher: Cambridge University Press
  publisher-place: Cambridge ; New York
  title: Lévy processes
  type: book

- id: BertoinSubordinators2000
  author:
    - family: Bertoin
      given: Jean
  citation-key: BertoinSubordinators2000
  issued:
    - year: 2000
  publisher: University of Aarhus. Centre for Mathematical Physics and Stochastics …
  title: >-
    Subordinators, Lévy processes with no negative jumps, and branching
    processes
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- id: BorovkovKendall2001
  accessed:
    - year: 2020
      month: 2
      day: 4
  author:
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      given: Konstantin
    - family: Burq
      given: Zaeem
  citation-key: BorovkovKendall2001
  container-title: Electronic Communications in Probability
  container-title-short: Electron. Commun. Probab.
  DOI: 10.1214/ECP.v6-1038
  ISSN: 1083-589X
  issued:
    - year: 2001
  language: EN
  page: 91-94
  title: Kendall's identity for the first crossing time revisited
  type: article-journal
  volume: '6'

- id: CinlarRepresentation1981
  accessed:
    - year: 2020
      month: 2
      day: 12
  author:
    - family: Çinlar
      given: E.
    - family: Jacod
      given: J.
  citation-key: CinlarRepresentation1981
  collection-title: Progress in Probability and Statistics
  container-title: Seminar on Stochastic Processes, 1981
  DOI: 10.1007/978-1-4612-3938-3_8
  editor:
    - family: Çinlar
      given: E.
    - family: Chung
      given: K. L.
    - family: Getoor
      given: R. K.
  event-place: Boston, MA
  ISBN: 978-1-4612-3938-3
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    - year: 1981
  language: en
  page: 159-242
  publisher: Birkhäuser
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  title: >-
    Representation of Semimartingale Markov Processes in Terms of Wiener
    Processes and Poisson Random Measures
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  URL: https://doi.org/10.1007/978-1-4612-3938-3_8

- id: DoneyFluctuation2007
  author:
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      given: Ronald A.
  call-number: QA274.73 .D66 2007
  citation-key: DoneyFluctuation2007
  collection-number: '1897'
  collection-title: Lecture notes in mathematics
  DOI: 10.1007/978-3-540-48511-7_9
  event-place: Berlin ; New York
  ISBN: 978-3-540-48510-0
  issued:
    - year: 2007
  number-of-pages: '147'
  publisher: Springer
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  title: >-
    Fluctuation theory for Lévy processes: ecole d’eté de probabilités de
    Saint-Flour XXXV, 2005
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  volume: '1897'

- id: GrigelionisStudent2013
  accessed:
    - year: 2021
      month: 11
      day: 17
  author:
    - family: Grigelionis
      given: Bronius
  citation-key: GrigelionisStudent2013
  collection-title: SpringerBriefs in Statistics
  DOI: 10.1007/978-3-642-31146-8
  event-place: Berlin, Heidelberg
  ISBN: 978-3-642-31145-1 978-3-642-31146-8
  issued:
    - year: 2013
  language: en
  publisher: Springer Berlin Heidelberg
  publisher-place: Berlin, Heidelberg
  title: Student’s t-Distribution and Related Stochastic Processes
  type: book
  URL: http://link.springer.com/10.1007/978-3-642-31146-8

- id: GrosswaldStudent1976
  accessed:
    - year: 2021
      month: 11
      day: 24
  author:
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      given: E.
  citation-key: GrosswaldStudent1976
  container-title: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
  container-title-short: Z. Wahrscheinlichkeitstheorie verw Gebiete
  DOI: 10.1007/BF00533993
  ISSN: 1432-2064
  issue: '2'
  issued:
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      month: 6
      day: 1
  language: en
  page: 103-109
  title: The student t-distribution of any degree of freedom is infinitely divisible
  type: article-journal
  volume: '36'

- id: IsmailBessel1977
  accessed:
    - year: 2021
      month: 11
      day: 24
  author:
    - family: Ismail
      given: Mourad E. H.
  citation-key: IsmailBessel1977
  container-title: The Annals of Probability
  DOI: 10.1214/aop/1176995766
  ISSN: 0091-1798, 2168-894X
  issue: '4'
  issued:
    - year: 1977
      month: 8
  page: 582-585
  publisher: Institute of Mathematical Statistics
  title: >-
    Bessel Functions and the Infinite Divisibility of the Student $t$-
    Distribution
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  volume: '5'

- id: JacobLevyType2001
  accessed:
    - year: 2020
      month: 2
      day: 4
  author:
    - family: Jacob
      given: Niels
    - family: Schilling
      given: René L.
  citation-key: JacobLevyType2001
  container-title: 'Lévy Processes: Theory and Applications'
  DOI: 10.1007/978-1-4612-0197-7_7
  editor:
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    - family: Mikosch
      given: Thomas
  event-place: Boston, MA
  ISBN: 978-1-4612-0197-7
  issued:
    - year: 2001
  language: en
  page: 139-168
  publisher: Birkhäuser
  publisher-place: Boston, MA
  title: Lévy-Type Processes and Pseudodifferential Operators
  type: chapter
  URL: https://doi.org/10.1007/978-1-4612-0197-7_7

- id: JacodTime1988
  accessed:
    - year: 2019
      month: 12
      day: 1
  author:
    - family: Jacod
      given: Jean
    - family: Protter
      given: Philip
  citation-key: JacodTime1988
  container-title: The Annals of Probability
  container-title-short: Ann. Probab.
  DOI: 10.1214/aop/1176991776
  ISSN: 0091-1798, 2168-894X
  issue: '2'
  issued:
    - year: 1988
      month: 4
  language: EN
  page: 620-641
  title: Time Reversal on Levy Processes
  type: article-journal
  volume: '16'

- id: KallenbergFoundations2002
  accessed:
    - year: 2020
      month: 2
      day: 11
  author:
    - family: Kallenberg
      given: Olav
  citation-key: KallenbergFoundations2002
  collection-title: Probability and Its Applications
  DOI: 10.1007/978-1-4757-4015-8
  edition: '2'
  event-place: New York
  ISBN: 978-0-387-95313-7
  issued:
    - year: 2002
  language: en
  publisher: Springer-Verlag
  publisher-place: New York
  title: Foundations of Modern Probability
  type: book
  URL: https://www.springer.com/gp/book/9780387953137

- id: KyprianouFluctuations2014
  author:
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      given: Andreas E.
  call-number: QA274.73 .K97 2014
  citation-key: KyprianouFluctuations2014
  collection-title: Universitext
  edition: Second edition
  event-place: Heidelberg
  ISBN: 978-3-642-37631-3
  issued:
    - year: 2014
  number-of-pages: '455'
  publisher: Springer
  publisher-place: Heidelberg
  title: 'Fluctuations of Lévy processes with applications: introductory lectures'
  type: book

- id: LeonenkoCorrelation2014
  accessed:
    - year: 2019
      month: 10
      day: 16
  author:
    - family: Leonenko
      given: Nikolai N
    - family: Meerschaert
      given: Mark M
    - family: Schilling
      given: René L
    - family: Sikorskii
      given: Alla
  citation-key: LeonenkoCorrelation2014
  container-title: Communications in Applied and Industrial Mathematics
  DOI: 10.1685/journal.caim.483
  ISSN: '20380909'
  issue: '1'
  issued:
    - year: 2014
      month: 10
      day: 30
  language: en
  title: Correlation Structure of Time-Changed Lévy Processes
  type: article-journal
  URL: http://caim.simai.eu/index.php/caim/article/view/483
  volume: '6'

- id: MeerschaertTriangular2008
  accessed:
    - year: 2019
      month: 6
      day: 16
  author:
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      given: Mark M.
    - family: Scheffler
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  citation-key: MeerschaertTriangular2008
  container-title: Stochastic Processes and their Applications
  container-title-short: Stochastic Processes and their Applications
  DOI: 10.1016/j.spa.2007.10.005
  ISSN: 0304-4149
  issue: '9'
  issued:
    - year: 2008
      month: 9
      day: 1
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  page: 1606-1633
  title: Triangular array limits for continuous time random walks
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  volume: '118'

- id: RubinsteinSimulation2016
  author:
    - family: Rubinstein
      given: Reuven Y.
    - family: Kroese
      given: Dirk P.
  citation-key: RubinsteinSimulation2016
  collection-title: Wiley series in probability and statistics
  edition: 3 edition
  event-place: Hoboken, New Jersey
  ISBN: 978-1-118-63216-1
  issued:
    - year: 2016
      month: 11
      day: 7
  language: English
  number-of-pages: '432'
  publisher: Wiley
  publisher-place: Hoboken, New Jersey
  title: Simulation and the Monte Carlo Method
  type: book

- id: SatoLevy1999
  author:
    - family: Sato
      given: Ken-iti
  citation-key: SatoLevy1999
  ISBN: 978-0-521-55302-5
  issued:
    - year: 1999
      month: 11
      day: 11
  language: en
  number-of-pages: '502'
  publisher: Cambridge University Press
  title: Lévy Processes and Infinitely Divisible Distributions
  type: book

- id: UnserIntroduction2014
  author:
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      given: Michael A.
    - family: Tafti
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  call-number: QA274.23 .U57 2014
  citation-key: UnserIntroduction2014
  event-place: New York
  ISBN: 978-1-107-05854-5
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    - year: 2014
  number-of-pages: '387'
  publisher: Cambridge University Press
  publisher-place: New York
  title: An introduction to sparse stochastic processes
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  URL: http://www.sparseprocesses.org/sparseprocesses-123456.pdf

- id: UnserUnified2014
  author:
    - family: Unser
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    - family: Tafti
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    - family: Amini
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    - family: Kirshner
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  citation-key: UnserUnified2014
  container-title: IEEE Transactions on Information Theory
  DOI: 10.1109/TIT.2014.2311903
  ISSN: 0018-9448
  issue: '5'
  issued:
    - year: 2014
      month: 5
  page: 3036-3051
  title: >-
    A unified formulation of Gaussian vs sparse stochastic processes - Part II:
    Discrete-domain theory
  type: article-journal
  URL: http://arxiv.org/abs/1108.6152
  volume: '60'

- id: UnserUnified2014a
  author:
    - family: Unser
      given: M.
    - family: Tafti
      given: P. D.
    - family: Sun
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  citation-key: UnserUnified2014a
  container-title: IEEE Transactions on Information Theory
  DOI: 10.1109/TIT.2014.2298453
  ISSN: 0018-9448
  issue: '3'
  issued:
    - year: 2014
      month: 3
  page: 1945-1962
  title: >-
    A unified formulation of Gaussian vs sparse stochastic processes—Part I:
    Continuous-domain theory
  type: article-journal
  URL: http://arxiv.org/abs/1108.6150
  volume: '60'

- id: UpadhyeUnified2020
  accessed:
    - year: 2021
      month: 3
      day: 31
  author:
    - family: Upadhye
      given: Neelesh S.
    - family: Barman
      given: Kalyan
  citation-key: UpadhyeUnified2020
  container-title: arXiv:2004.07593 [math]
  issued:
    - year: 2020
      month: 7
      day: 29
  title: A Unified Approach to Stein's Method for Stable Distributions
  type: article-journal
  URL: http://arxiv.org/abs/2004.07593

- id: VeilletteNumerical2010
  accessed:
    - year: 2019
      month: 6
      day: 16
  author:
    - family: Veillette
      given: Mark
    - family: Taqqu
      given: Murad S.
  citation-key: VeilletteNumerical2010
  container-title: Methodology and Computing in Applied Probability
  container-title-short: Methodol Comput Appl Probab
  DOI: 10.1007/s11009-009-9158-y
  ISSN: 1573-7713
  issue: '4'
  issued:
    - year: 2010
      month: 12
      day: 1
  language: en
  number: '4'
  page: 695-729
  title: Numerical Computation of First-Passage Times of Increasing Lévy Processes
  type: article-journal
  URL: http://arxiv.org/abs/0904.4232
  volume: '12'

- id: VeilletteUsing2010
  accessed:
    - year: 2019
      month: 6
      day: 16
  author:
    - family: Veillette
      given: Mark
    - family: Taqqu
      given: Murad S.
  citation-key: VeilletteUsing2010
  container-title: Statistics & Probability Letters
  container-title-short: Statistics & Probability Letters
  DOI: 10.1016/j.spl.2010.01.002
  ISSN: 0167-7152
  issue: '7'
  issued:
    - year: 2010
      month: 4
      day: 1
  number: '7'
  page: 697-705
  title: >-
    Using differential equations to obtain joint moments of first-passage times
    of increasing Lévy processes
  type: article-journal
  URL: http://arxiv.org/abs/0906.5083
  volume: '80'

- id: WasanInverse1968
  accessed:
    - year: 2020
      month: 10
      day: 11
  author:
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      given: M. T.
  citation-key: WasanInverse1968
  container-title: Scandinavian Actuarial Journal
  container-title-short: Scandinavian Actuarial Journal
  DOI: 10.1080/03461238.1968.10413264
  ISSN: 0346-1238, 1651-2030
  issue: 1-2
  issued:
    - year: 1968
      month: 1
  language: en
  page: 69-96
  title: On an inverse Gaussian process
  type: article-journal
  volume: '1968'

- id: WolpertLecture2021
  accessed:
    - year: 2021
      month: 12
      day: 2
  author:
    - family: Wolpert
      given: Robert L.
  citation-key: WolpertLecture2021
  container-title: arXiv:2106.00087 [math]
  issued:
    - year: 2021
      month: 5
      day: 31
  title: Lecture Notes on Stationary Gamma Processes
  type: article-journal
  URL: http://arxiv.org/abs/2106.00087

- id: XuCalibrating2019
  accessed:
    - year: 2020
      month: 12
      day: 16
  author:
    - family: Xu
      given: Kailai
    - family: Darve
      given: Eric
  citation-key: XuCalibrating2019
  container-title: arXiv:1812.08883 [cs, stat]
  issued:
    - year: 2019
      month: 9
      day: 26
  title: Calibrating Multivariate Lévy Processes with Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1812.08883
...
