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references.bib
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@book{adams1995hitchhiker,
title={The Hitchhiker's Guide to the Galaxy},
author={Adams, D.},
isbn={9781417642595},
url={http://books.google.com/books?id=W-xMPgAACAAJ},
year={1995},
publisher={San Val}
}
@book{spivak,
title={Calculus on Manifolds},
author={Michael Spivak},
volume={1},
year={1965},
publisher={WA Benjamin New York}
}
@book{Davis,
title={Fourier series and orthogonal functions},
author={Harry F. Davis}
}
@book{Shifrin2015,
title={Differential geometry: a first course in curves and surfaces},
author={Theodore Shifrin}
}
@book{Walschap,
title={Multivariable calculus and differential geometry},
author={Gerard Walschap}
}
@book{walschap2015multivariable,
title={Multivariable Calculus and Differential Geometry},
author={Walschap, G.},
isbn={9783110369540},
series={De Gruyter Textbook},
url={https://books.google.com/books?id=cXPyCQAAQBAJ},
year={2015},
publisher={De Gruyter}
}
@book{Mendelson,
title={Introduction to topology},
author={Bert Mendelson}
}
@article{Fletcher,
title={Gaussian Distributions on Lie Groups and Their Application to Statistical Shape Analysis},
author={P. Thomas Fletcher et al}
}
@article{Xu2012,
file = {:C$\backslash$:/Users/yuguangyang/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Xu, Ma - 2012 - Applications of Lie groups and Lie algebra to computer vision A brief survey.pdf:pdf},
isbn = {978-1-4673-0199-2},
journal = {Systems and Informatics (ICSAI), 2012 International Conference on},
keywords = {lie algebra,lie groups,transformation matrix},
mendeley-groups = {ModernMath},
number = {Icsai},
pages = {2024--2029},
title = {{Applications of Lie groups and Lie algebra to computer vision: A brief survey}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6223449},
year = {2012}
}
@article{Manton2013,
journal = {IEEE Journal of Selected Topics in Signal Processing},
number = {4},
pages = {681--699},
title = {A Primer on Stochastic Differential Geometry for Signal Processing},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6519312},
volume = {7},
year = {2013}
}
@article{Pennec2006,
author = {Pennec, Xavier},
doi = {10.1007/s10851-006-6228-4},
file = {:home/yuguangyang/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pennec - 2006 - Intrinsic statistics on Riemannian manifolds Basic tools for geometric measurements.pdf:pdf;:home/yuguangyang/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pennec - 2006 - Intrinsic statistics on Riemannian manifolds Basic tools for geometric measurements(2).pdf:pdf},
isbn = {975 518 133 4},
issn = {09249907},
journal = {Journal of Mathematical Imaging and Vision},
keywords = {Computing on manifolds,Covariance,Frechet mean,Geometry,Riemannian manifolds,Statistics},
mendeley-groups = {ModernMath},
number = {1},
pages = {127--154},
title = {{Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements}},
volume = {25},
year = {2006}
}
@book{chirikjian2011stochastic,
title={Stochastic Models, Information Theory, and Lie Groups, Volume 2: Analytic Methods and Modern Applications},
author={Chirikjian, Gregory S},
volume={2},
year={2011},
publisher={Springer Science \& Business Media}
}
@book{chirikjian2011stochastic1,
title={Stochastic Models, Information Theory, and Lie Groups, Volume 1: Classical Results and Geometric Methods},
author={Chirikjian, Gregory S},
volume={1},
year={2011},
publisher={Springer Science \& Business Media}
}
@book{rosenthal2006first,
title={A first look at rigorous probability theory},
author={Rosenthal, Jeffrey Seth},
year={2006},
publisher={World Scientific}
}
@article{hoggintroduction,
title={Introduction to Mathematical Statistics, 7 ed},
author={Hogg, Robert V and McKean, Joseph and Craig, Allen T},
publisher={Pearson Education},
year={2012},
}
@misc{ wiki:Dirichlet,
author = "Wikipedia",
title = "Dirichlet conditions --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Dirichlet_conditions&oldid=699962273",
note = "[Online; accessed 17-May-2016]"
}
@misc{ wiki:continuous,
author = "Wikipedia",
title = "Continuous function --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "\url{https://en.wikipedia.org/w/index.php?title=Continuous_function&oldid=719749891}",
note = "[Online; accessed 17-May-2016]"
}
@article{chirikjianstochastic,
title={STOCHASTIC MODELS, INFORMATION THEORY, AND LIE GROUPS, Vol 1.},
author={Chirikjian, GS}
}
@book{mathanalysischinese,
title={mathematical analysis (Chinese)},
author={XuaDong normal university},
year={2001},
publisher={higher education press}
}
@article{prosperetti2013advanced,
title={Advanced mathematics for applications},
author={Prosperetti, Andrea},
journal={SIAM Review Vol. 55, Issue 2 (June 2013)},
volume={55},
number={2},
pages={403},
year={2013},
publisher={SIAM}
}
@book{davis1989fourier,
title={Fourier series and orthogonal functions},
author={Davis, Harry F},
year={1989},
publisher={Courier Corporation}
}
@book{krim2015geometric,
title={Geometric methods in signal and image analysis},
author={Krim, Hamid and Hamza, Abdessamad Ben},
year={2015},
publisher={Cambridge University Press}
}
@misc{ wiki:homomorphism,
author = "Wikipedia",
title = "Homomorphism --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "\url{https://en.wikipedia.org/w/index.php?title=Homomorphism&oldid=699443243}",
note = "[Online; accessed 17-May-2016]"
}
@inproceedings{long2012banana,
title={The Banana Distribution is Gaussian: A Localization Study with Exponential Coordinates.},
author={Long, Andrew W and Wolfe, Kevin C and Mashner, Michael and Chirikjian, Gregory S},
booktitle={Robotics: science and systems},
year={2012}
}
@book{stefanica2008primer,
title={A primer for the Mathematics of Financial Engineering},
author={Stefanica, Dan},
year={2008},
publisher={Fe Press}
}
@misc{ wiki:Borelset,
author = "Wikipedia",
title = "Borel set --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "\url{https://en.wikipedia.org/w/index.php?title=Borel_set&oldid=697808826}",
note = "[Online; accessed 18-May-2016]"
}
@book{fries2007mathematical,
title={Mathematical finance: theory, modeling, implementation},
author={Fries, Christian},
year={2007},
publisher={John Wiley \& Sons}
}
@misc{ wiki:measure,
author = "Wikipedia",
title = "Measure (mathematics) --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Measure_(mathematics)&oldid=705572763",
note = "[Online; accessed 18-May-2016]"
}
@book{rosenthal2006first,
title={A first look at rigorous probability theory},
author={Rosenthal, Jeffrey Seth},
year={2006},
publisher={World Scientific}
}
@misc{ wiki:openset,
author = "Wikipedia",
title = "Open set --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Open_set&oldid=720273499",
note = "[Online; accessed 22-May-2016]"
}
@book{dineen2013probability,
title={Probability theory in finance: a mathematical guide to the Black-Scholes formula},
author={Dineen, Se{\'a}n},
volume={70},
year={2013},
publisher={American Mathematical Soc.}
}
@book{neftci2000introduction,
title={An introduction to the mathematics of financial derivatives},
author={Neftci, Salih N},
year={2000},
publisher={Academic Press}
}
@book{carter2001foundations,
title={Foundations of mathematical economics},
author={Carter, Michael},
year={2001},
publisher={MIT Press}
}
@article{de2012understanding,
title={Understanding convergence concepts: A visual-minded and graphical simulation-based approach},
author={De Micheaux, Pierre Lafaye and Liquet, Benoit},
journal={The American Statistician},
year={2012},
publisher={Taylor \& Francis}
}
@article{johnsonbaugh2010foundations,
title={Foundations of mathematical analysis},
author={Johnsonbaugh, Richard and Pfaffenberger, WE},
year={2010},
publisher={Dover}
}
@book{butcher2008numerical,
title={Numerical Methods for Ordinary Differential Equations},
author={Butcher, J.C.},
isbn={9780470753750},
url={https://books.google.com/books?id=opd2NkBmMxsC},
year={2008},
publisher={Wiley}
}
@book{glasserman2003monte,
title={Monte Carlo methods in financial engineering},
author={Glasserman, Paul},
volume={53},
year={2003},
publisher={Springer Science \& Business Media}
}
@misc{ wiki:closeset,
author = "Wikipedia",
title = "Closed set --- Wikipedia{,} The Free Encyclopedia",
year = "2015",
url = "https://en.wikipedia.org/w/index.php?title=Closed_set&oldid=681209723",
note = "[Online; accessed 25-May-2016]"
}
@book{rynne2000linear,
title={Linear functional analysis},
author={Rynne, Bryan P and Youngson, Martin A},
year={2000},
publisher={Springer Science \& Business Media}
}
@misc{ wiki:parseval,
author = "Wikipedia",
title = "Parseval's identity --- Wikipedia{,} The Free Encyclopedia",
year = "2015",
url = "https://en.wikipedia.org/w/index.php?title=Parseval%27s_identity&oldid=674669547",
note = "[Online; accessed 27-May-2016]"
}
@book{casella2002statistical,
title={Statistical inference},
author={Casella, George and Berger, Roger L},
volume={2},
year={2002},
publisher={Duxbury Pacific Grove, CA}
}
@article{jordan2002discriminative,
title={On discriminative vs. generative classifiers: A comparison of logistic regression and naive bayes},
author={Jordan, A},
journal={Advances in neural information processing systems},
volume={14},
pages={841},
year={2002}
}
@book{michalski2013machine,
title={Machine learning: An artificial intelligence approach},
author={Michalski, Ryszard S and Carbonell, Jaime G and Mitchell, Tom M},
year={2013},
publisher={Springer Science \& Business Media}
}
@misc{mitchell1997machine,
title={Machine learning. WCB},
author={Mitchell, Tom M and others},
year={1997},
publisher={McGraw-Hill Boston, MA:}
}
@book{cover2012elements,
title={Elements of information theory},
author={Cover, Thomas M and Thomas, Joy A},
year={2012},
publisher={John Wiley \& Sons}
}
@misc{ wiki:uniformcontinuity,
author = "Wikipedia",
title = "Uniform continuity --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Uniform_continuity&oldid=720971927",
note = "[Online; accessed 29-May-2016]"
}
@article{rasmussen2006gaussian,
title={Gaussian processes for machine learning},
author={Rasmussen, Carl Edward},
year={2006},
publisher={Citeseer}
}
@article{ankan2015mastering,
title={Mastering probabilistic graphical models using Python},
author={Ankan, Ankur and Panda, Abinash},
year={2015},
publisher={Packt Publ.}
}
@book{moon2000mathematical,
title={Mathematical methods and algorithms for signal processing},
author={Moon, Todd K Stirling and Wynn, C},
number={621.39: 51 MON},
year={2000}
}
@misc{ wiki:lebesgueintegral,
author = "Wikipedia",
title = "Lebesgue integration --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Lebesgue_integration&oldid=717765273",
note = "[Online; accessed 2-June-2016]"
}
@book{shreve2004stochastic2,
title={Stochastic calculus for finance II: Continuous-time models},
author={Shreve, Steven E},
volume={11},
year={2004},
publisher={Springer Science \& Business Media}
}
@book{shreve2004stochastic1,
title={Stochastic Calculus for Finance I: The Binomial Asset Pricing Model},
author={Shreve, Steven},
year={2004},
publisher={Springer Science \& Business Media}
}
@misc{ wiki:conditionalExp,
author = "Wikipedia",
title = "Conditional expectation --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
url = "https://en.wikipedia.org/w/index.php?title=Conditional_expectation&oldid=721270714",
note = "[Online; accessed 7-June-2016]"
}
@book{kreyszig1989introductory,
title={Introductory functional analysis with applications},
author={Kreyszig, Erwin},
volume={81},
year={1989},
publisher={wiley New York}
}
@book{meyer2000matrix,
title={Matrix analysis and applied linear algebra},
author={Meyer, Carl D},
volume={2},
year={2000},
publisher={Siam}
}
@book{williams1991probability,
title={Probability with martingales},
author={Williams, David},
year={1991},
publisher={Cambridge university press}
}
@book{calafiore2014optimization,
title={Optimization Models},
author={Calafiore, Giuseppe C and El Ghaoui, Laurent},
year={2014},
publisher={Cambridge university press}
}
@book{Robinson2015nonlinear,
title={Nonlinear optimization I lecture notes},
author={Robinson,Daniel},
year={2015},
publisher={Johns Hopkins University}
}
@book{Robinson2015nonlinear2,
title={Nonlinear optimization II lecture notes},
author={Robinson,Daniel},
year={2015},
publisher={Johns Hopkins University}
}
@book{Robinson2015convex,
title={Convex optimization lecture notes},
author={Robinson,Daniel},
year={2015},
publisher={Johns Hopkins University}
}
@book{Holmes-Cerfon2015applied,
title={Applied Stochastic Analysis lecture notes},
author={Miranda, Holmes-Cerfon},
year={2015},
publisher={NewYork University}
}
@inproceedings{pighin2007practical,
title={Practical least-squares for computer graphics: Video files associated with this course are available from the citation page},
author={Pighin, Fred and Lewis, John P},
booktitle={ACM SIGGRAPH 2007 courses},
pages={1--57},
year={2007},
organization={ACM}
}
@book{Lalley2001mathematical,
title={The mathematics of financial derivatives: a student introduction},
author={Steve Lalley},
year={2001},
publisher={Chicago University Statistics 390/ Mathematical Finance 345}
}
@book{shreve2012stochastic1,
title={Stochastic Calculus for Finance I: The Binomial Asset Pricing Model},
author={Shreve, Steven},
year={2012},
publisher={Springer Science \& Business Media}
}
@book{shreve2004stochastic2,
title={Stochastic calculus for finance II: Continuous-time models},
author={Shreve, Steven E},
volume={11},
year={2004},
publisher={Springer Science \& Business Media}
}
@book{khalil1996nonlinear,
title={Nonlinear systems, 3rd edition},
author={Khalil, Hassan K},
volume={3},
year={2002},
publisher={Prentice Hall}
}
@book{Sigman2009stochastic,
title={Stochastic modeling I lecture notes},
author={Karl, Sigman},
year={2009},
publisher={Columbia University}
}
@book{mitzenmacher2005probability,
title={Probability and computing: Randomized algorithms and probabilistic analysis},
author={Mitzenmacher, Michael and Upfal, Eli},
year={2005},
publisher={Cambridge University Press}
}
@book{luenberger1979introduction,
title={Introduction to dynamic systems: theory, models, and applications},
author={Luenberger, D},
year={1979},
publisher={Wiley}
}
@misc{ wiki:markovprocess,
author = "Wikipedia",
title = "Markov process --- Wikipedia{,} The Free Encyclopedia",
year = "2016",
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