Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste
ilustraciones, diagramas
- Autores:
-
Rangel Gutiérrez, Jhonier Sebastian
- Tipo de recurso:
- Fecha de publicación:
- 2024
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/86172
- Palabra clave:
- 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Puente browniano
Puente browniano fraccional
Puente gaussiano
Estimación
Simulación mediante métodos numéricos
Método de Euler-Maruyama
Método de Cholesky
Brownian bridge
Fractional brownian bridge
Gaussian bridge
Estimation
Simulation by numerical methods
Euler-Maruyama method
Cholesky method
estocástica
Bondad de ajuste
Puente browniano
stochastic
goodness of fit
Brownian bridge
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| dc.title.translated.eng.fl_str_mv |
Comparative analysis of stochastic bridges: simulation, estimation and goodness of fit |
| title |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| spellingShingle |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Puente browniano Puente browniano fraccional Puente gaussiano Estimación Simulación mediante métodos numéricos Método de Euler-Maruyama Método de Cholesky Brownian bridge Fractional brownian bridge Gaussian bridge Estimation Simulation by numerical methods Euler-Maruyama method Cholesky method estocástica Bondad de ajuste Puente browniano stochastic goodness of fit Brownian bridge |
| title_short |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| title_full |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| title_fullStr |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| title_full_unstemmed |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| title_sort |
Análisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajuste |
| dc.creator.fl_str_mv |
Rangel Gutiérrez, Jhonier Sebastian |
| dc.contributor.advisor.spa.fl_str_mv |
Arunachalam, Viswanathan |
| dc.contributor.author.spa.fl_str_mv |
Rangel Gutiérrez, Jhonier Sebastian |
| dc.contributor.orcid.spa.fl_str_mv |
Rangel Gutiérrez, Jhonier [0000-0002-6849-5551] |
| dc.contributor.cvlac.spa.fl_str_mv |
https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0002034802 |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas |
| topic |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Puente browniano Puente browniano fraccional Puente gaussiano Estimación Simulación mediante métodos numéricos Método de Euler-Maruyama Método de Cholesky Brownian bridge Fractional brownian bridge Gaussian bridge Estimation Simulation by numerical methods Euler-Maruyama method Cholesky method estocástica Bondad de ajuste Puente browniano stochastic goodness of fit Brownian bridge |
| dc.subject.proposal.spa.fl_str_mv |
Puente browniano Puente browniano fraccional Puente gaussiano Estimación Simulación mediante métodos numéricos Método de Euler-Maruyama Método de Cholesky Brownian bridge |
| dc.subject.proposal.eng.fl_str_mv |
Fractional brownian bridge Gaussian bridge Estimation Simulation by numerical methods Euler-Maruyama method Cholesky method |
| dc.subject.wikidata.spa.fl_str_mv |
estocástica Bondad de ajuste Puente browniano |
| dc.subject.wikidata.eng.fl_str_mv |
stochastic goodness of fit Brownian bridge |
| description |
ilustraciones, diagramas |
| publishDate |
2024 |
| dc.date.accessioned.none.fl_str_mv |
2024-05-28T21:32:20Z |
| dc.date.available.none.fl_str_mv |
2024-05-28T21:32:20Z |
| dc.date.issued.none.fl_str_mv |
2024-05-28 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
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Text |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/86172 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/86172 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
| dc.relation.references.spa.fl_str_mv |
ARAGÓN URREGO, Daniel: Valoración de opciones americanas por el método de malla estocástica bajo movimiento Browniano fraccional del activo subyacente (American Option Pricing by the Stochastic Mesh Method Under Fractional Brownian Movement of the Underlying Asset). (2018) BRAS, Pierre ; KOHATSU-HIGA, Arturo: Simulation of reflected Brownian motion on two dimensional wedges. In: Stochastic Processes and their Applications 156 (2023), S. 349–378 CARLSON, Max ; KIRBY, Robert M. ; SUNDAR, Hari: A scalable framework for solving fractional diffusion equations. In: Proceedings of the 34th ACM International Conference on Supercomputing, 2020, S. 1–11 CASELLA, George ; FERRÁNDIZ, Juan ; PEÑA, Daniel ; INSUA, David R. ; BERNARDO, José M ; GARCÍA-LÓPEZ, PA ; GONZÁLEZ, A ; BERGER, J ; DAWID, AP ; DICICCIO, Thomas J. u. a.: Statistical inference and Monte Carlo algorithms. In: Test 5 (1996), S. 249–344 CASTAÑEDA, Liliana B. ; ARUNACHALAM, Viswanathan ; DHARMARAJA, Selvamuthu: Introduction to probability and stochastic processes with applications. John Wiley & Sons, 2012 CHOW, Winston C.: Brownian bridge. In: Wiley interdisciplinary reviews: computational statistics 1 (2009), Nr. 3, S. 325–332 COOK, R D.: Envelope methods. In: Wiley Interdisciplinary Reviews: Computational Statistics 12 (2020), Nr. 2, S. e1484 DASGUPTA, Anirban: Asymptotic theory of statistics and probability. Bd. 180. Springer, 2008 DIEKER, Ton: Simulation of fractional Brownian motion, Masters Thesis, Department of Mathematical Sciences, University of Twente …, Diss., 2004 EMBRECHTS, Paul ; MAEJIMA, Makoto: An introduction to the theory of self-similar stochastic processes. In: International journal of modern physics B 14 (2000), Nr. 12n13, S. 1399–1420 FRIEDRICH, Jan ; GALLON, Sebastian ; PUMIR, Alain ; GRAUER, Rainer: Stochastic interpolation of sparsely sampled time series via multipoint fractional Brownian bridges. In: Physical Review Letters 125 (2020), Nr. 17, S. 170602 GOLDSMITH, Jeff ; GREVEN, Sonja ; CRAINICEANU, CIPRIAN: Corrected confidence bands for functional data using principal components. In: Biometrics 69 (2013), Nr. 1, S. 41–51 GORGENS, Maik: Conditioning of Gaussian processes and a zero area Brownian bridge. In: arXiv preprint arXiv:1302.4186 (2013) GOSSET, William S.: William Sealy Gosset. In: Biographical Encyclopedia of Mathematicians 1 (1908), S. 239 HOLLANDER, Myles ; WOLFE, Douglas A. ; CHICKEN, Eric: Nonparametric statistical methods. John Wiley & Sons, 2013 KOKOSZKA, Piotr ; REIMHERR, Matthew: Introduction to functional data analysis. CRC press, 2017 KOLMOGOROV, Andrei N.: Wienersche spiralen und einige andere interessante kurven in hilbertscen raum, cr (doklady). In: Acad. Sci. URSS (NS) 26 (1940), S. 115–118 KRANSTAUBER, Bart ; KAYS, Roland ; LAPOINT, Scott D. ; WIKELSKI, Martin ; SAFI, Kamran: A dynamic Brownian bridge movement model to estimate utilization distributions for heterogeneous animal movement. In: Journal of Animal Ecology 81 (2012), Nr. 4, S. 738–746 LAMPERTI, John: Semi-stable stochastic processes. In: Transactions of the American mathematical Society 104 (1962), Nr. 1, S. 62–78 MALLIAVIN, Paul: Stochastic analysis. Bd. 313. Springer, 2015 MANSUY, Roger ; YOR, Marc: Aspects of Brownian motion. Springer Science & Business Media, 2008 NAPIERALA, Matthew A.: What is the Bonferroni correction? In: Aaos Now (2012), S. 40–41 NUALART, David: The Malliavin calculus and related topics. Bd. 1995. Springer, 2006 ØKSENDAL, Bernt ; ØKSENDAL, Bernt: Stochastic differential equations. Springer, 2003 ÖZAK, Myriam M. n. ; CASTAÑEDA, Liliana B.: Introducción a la teoría avanzada de la probabilidad. Bd. 2. Univ. Nacional de Colombia, 2002 RAJU, Tonse N.: William Sealy Gosset and William A. Silverman: two “students” of science. In: Pediatrics 116 (2005), Nr. 3, S. 732–735 RINCÓN, Luis: Introducción a los procesos estocásticos. UNAM, Facultad de Ciencias, 2012 RINCÓN, Luis: Introducción a la probabilidad. (2014) ROSTEK, S ; SCHÖBEL, R: A note on the use of fractional Brownian motion for financial modeling. In: Economic Modelling 30 (2013), S. 30–35 SRIVASTAVA, Muni S.: Multivariate theory for analyzing high dimensional data. In: Journal of the Japan Statistical Society 37 (2007), Nr. 1, S. 53–86 SURYAWAN, Herry P. ; GUNARSO, Boby: Self-intersection local times of generalized mixed fractional Brownian motion as white noise distributions. In: Journal of Physics: Conference Series Bd. 855 IOP Publishing, 2017, S. 012050 TAQQU, Murad: Weak convergence to fractional Brownian motion and to the Rosenblatt process. In: Advances in Applied Probability 7 (1975), Nr. 2, S. 249–249 WANG, Jian ; LIN, Dongding ; LI, Wenjie: Dialogue Planning via Brownian Bridge Stochastic Process for Goal-directed Proactive Dialogue. In: arXiv preprint arXiv:2305.05290 (2023) WANG, Shiyan ; RAMKRISHNA, Doraiswami ; NARSIMHAN, Vivek: Exact sampling of polymer conformations using Brownian bridges. In: The Journal of Chemical Physics 153 (2020), Nr. 3, S. 034901 WASSERMAN, Larry: All of nonparametric statistics. Springer Science & Business Media, 2006 WEI, Bo-Cheng: Exponential family nonlinear models. Bd. 1. Springer, 1998 XU, Mengjia: Understanding graph embedding methods and their applications. In: SIAM Review 63 (2021), Nr. 4, S. 825–853 YERLIKAYA-ÖZKURT, Fatma ; VARDAR-ACAR, Ceren ; YOLCU-OKUR, Yeliz ; WEBER, G-W: Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method. In: Journal of Computational and Applied Mathematics 259 (2014), S. 843–850 YUAN, Chenggui ; MAO, Xuerong: Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching. In: Mathematics and Computers in Simulation 64 (2004), Nr. 2, S. 223–235 ZHU, Chenyao ; LUO, Lan ; LI, Rui ; GUO, Junhui ; WANG, Qining: Wearable Motion Analysis System for Thoracic Spine Mobility with Inertial Sensors. In: IEEE Transactions on Neural Systems and Rehabilitation Engineering (2024) |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Estadística |
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Facultad de Ciencias |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Arunachalam, Viswanathanc4c758748e94de0301844d7c2a049050Rangel Gutiérrez, Jhonier Sebastianac72c77799c4e63eb9b7e4d5d3babced600Rangel Gutiérrez, Jhonier [0000-0002-6849-5551]https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=00020348022024-05-28T21:32:20Z2024-05-28T21:32:20Z2024-05-28https://repositorio.unal.edu.co/handle/unal/86172Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasEn este trabajo se presenta un análisis comparativo entre el puente browniano clásico y puentes brownianos fraccionarios con diferentes parámetros de Hurst. También se aborda un enfoque para la inferencia clásica sobre los parámetros de estos modelos. Se explica además cómo simular estos procesos cuando los parámetros ya son conocidos o estimados. Asimismo, se describe una metodología para llevar a cabo pruebas de bondad de ajuste mediante el uso de técnicas de envolvimiento. Por último, se presentan tres aplicaciones en datos funcionales, estadística espacial y procesamiento del lenguaje natural. (Texto tomado de la fuente).This work presents a comparative analysis between the classic Brownian bridge and fractional Brownian bridges with different Hurst parameters. It also introduces an approach to classical inference on the parameters of these models. The simulation of these processes is explained when the parameters are either known or estimated. Additionally, a method for conducting goodness-of-fit tests using the envelopment technique is discussed. Finally, three applications in functional data, spatial statistics, and natural language processing are presented.MaestríaMagíster en Ciencias - Estadísticaviii, 63 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasPuente brownianoPuente browniano fraccionalPuente gaussianoEstimaciónSimulación mediante métodos numéricosMétodo de Euler-MaruyamaMétodo de CholeskyBrownian bridgeFractional brownian bridgeGaussian bridgeEstimationSimulation by numerical methodsEuler-Maruyama methodCholesky methodestocásticaBondad de ajustePuente brownianostochasticgoodness of fitBrownian bridgeAnálisis comparativo de los puentes estocásticos: simulación, estimación y bondad de ajusteComparative analysis of stochastic bridges: simulation, estimation and goodness of fitTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMARAGÓN URREGO, Daniel: Valoración de opciones americanas por el método de malla estocástica bajo movimiento Browniano fraccional del activo subyacente (American Option Pricing by the Stochastic Mesh Method Under Fractional Brownian Movement of the Underlying Asset). (2018)BRAS, Pierre ; KOHATSU-HIGA, Arturo: Simulation of reflected Brownian motion on two dimensional wedges. In: Stochastic Processes and their Applications 156 (2023), S. 349–378CARLSON, Max ; KIRBY, Robert M. ; SUNDAR, Hari: A scalable framework for solving fractional diffusion equations. In: Proceedings of the 34th ACM International Conference on Supercomputing, 2020, S. 1–11CASELLA, George ; FERRÁNDIZ, Juan ; PEÑA, Daniel ; INSUA, David R. ; BERNARDO, José M ; GARCÍA-LÓPEZ, PA ; GONZÁLEZ, A ; BERGER, J ; DAWID, AP ; DICICCIO, Thomas J. u. a.: Statistical inference and Monte Carlo algorithms. In: Test 5 (1996), S. 249–344CASTAÑEDA, Liliana B. ; ARUNACHALAM, Viswanathan ; DHARMARAJA, Selvamuthu: Introduction to probability and stochastic processes with applications. John Wiley & Sons, 2012CHOW, Winston C.: Brownian bridge. In: Wiley interdisciplinary reviews: computational statistics 1 (2009), Nr. 3, S. 325–332COOK, R D.: Envelope methods. In: Wiley Interdisciplinary Reviews: Computational Statistics 12 (2020), Nr. 2, S. e1484DASGUPTA, Anirban: Asymptotic theory of statistics and probability. Bd. 180. Springer, 2008DIEKER, Ton: Simulation of fractional Brownian motion, Masters Thesis, Department of Mathematical Sciences, University of Twente …, Diss., 2004EMBRECHTS, Paul ; MAEJIMA, Makoto: An introduction to the theory of self-similar stochastic processes. In: International journal of modern physics B 14 (2000), Nr. 12n13, S. 1399–1420FRIEDRICH, Jan ; GALLON, Sebastian ; PUMIR, Alain ; GRAUER, Rainer: Stochastic interpolation of sparsely sampled time series via multipoint fractional Brownian bridges. In: Physical Review Letters 125 (2020), Nr. 17, S. 170602GOLDSMITH, Jeff ; GREVEN, Sonja ; CRAINICEANU, CIPRIAN: Corrected confidence bands for functional data using principal components. In: Biometrics 69 (2013), Nr. 1, S. 41–51GORGENS, Maik: Conditioning of Gaussian processes and a zero area Brownian bridge. In: arXiv preprint arXiv:1302.4186 (2013)GOSSET, William S.: William Sealy Gosset. In: Biographical Encyclopedia of Mathematicians 1 (1908), S. 239HOLLANDER, Myles ; WOLFE, Douglas A. ; CHICKEN, Eric: Nonparametric statistical methods. John Wiley & Sons, 2013KOKOSZKA, Piotr ; REIMHERR, Matthew: Introduction to functional data analysis. CRC press, 2017KOLMOGOROV, Andrei N.: Wienersche spiralen und einige andere interessante kurven in hilbertscen raum, cr (doklady). In: Acad. Sci. URSS (NS) 26 (1940), S. 115–118KRANSTAUBER, Bart ; KAYS, Roland ; LAPOINT, Scott D. ; WIKELSKI, Martin ; SAFI, Kamran: A dynamic Brownian bridge movement model to estimate utilization distributions for heterogeneous animal movement. In: Journal of Animal Ecology 81 (2012), Nr. 4, S. 738–746LAMPERTI, John: Semi-stable stochastic processes. In: Transactions of the American mathematical Society 104 (1962), Nr. 1, S. 62–78MALLIAVIN, Paul: Stochastic analysis. Bd. 313. Springer, 2015MANSUY, Roger ; YOR, Marc: Aspects of Brownian motion. Springer Science & Business Media, 2008NAPIERALA, Matthew A.: What is the Bonferroni correction? In: Aaos Now (2012), S. 40–41NUALART, David: The Malliavin calculus and related topics. Bd. 1995. Springer, 2006ØKSENDAL, Bernt ; ØKSENDAL, Bernt: Stochastic differential equations. Springer, 2003ÖZAK, Myriam M. n. ; CASTAÑEDA, Liliana B.: Introducción a la teoría avanzada de la probabilidad. Bd. 2. Univ. Nacional de Colombia, 2002RAJU, Tonse N.: William Sealy Gosset and William A. Silverman: two “students” of science. In: Pediatrics 116 (2005), Nr. 3, S. 732–735RINCÓN, Luis: Introducción a los procesos estocásticos. UNAM, Facultad de Ciencias, 2012RINCÓN, Luis: Introducción a la probabilidad. (2014)ROSTEK, S ; SCHÖBEL, R: A note on the use of fractional Brownian motion for financial modeling. In: Economic Modelling 30 (2013), S. 30–35SRIVASTAVA, Muni S.: Multivariate theory for analyzing high dimensional data. In: Journal of the Japan Statistical Society 37 (2007), Nr. 1, S. 53–86SURYAWAN, Herry P. ; GUNARSO, Boby: Self-intersection local times of generalized mixed fractional Brownian motion as white noise distributions. In: Journal of Physics: Conference Series Bd. 855 IOP Publishing, 2017, S. 012050TAQQU, Murad: Weak convergence to fractional Brownian motion and to the Rosenblatt process. In: Advances in Applied Probability 7 (1975), Nr. 2, S. 249–249WANG, Jian ; LIN, Dongding ; LI, Wenjie: Dialogue Planning via Brownian Bridge Stochastic Process for Goal-directed Proactive Dialogue. In: arXiv preprint arXiv:2305.05290 (2023)WANG, Shiyan ; RAMKRISHNA, Doraiswami ; NARSIMHAN, Vivek: Exact sampling of polymer conformations using Brownian bridges. In: The Journal of Chemical Physics 153 (2020), Nr. 3, S. 034901WASSERMAN, Larry: All of nonparametric statistics. Springer Science & Business Media, 2006WEI, Bo-Cheng: Exponential family nonlinear models. Bd. 1. Springer, 1998XU, Mengjia: Understanding graph embedding methods and their applications. In: SIAM Review 63 (2021), Nr. 4, S. 825–853YERLIKAYA-ÖZKURT, Fatma ; VARDAR-ACAR, Ceren ; YOLCU-OKUR, Yeliz ; WEBER, G-W: Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method. In: Journal of Computational and Applied Mathematics 259 (2014), S. 843–850YUAN, Chenggui ; MAO, Xuerong: Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching. In: Mathematics and Computers in Simulation 64 (2004), Nr. 2, S. 223–235ZHU, Chenyao ; LUO, Lan ; LI, Rui ; GUO, Junhui ; WANG, Qining: Wearable Motion Analysis System for Thoracic Spine Mobility with Inertial Sensors. In: IEEE Transactions on Neural Systems and Rehabilitation Engineering (2024)InvestigadoresPúblico generalORIGINALTRABAJO_FINAL (50).pdfTRABAJO_FINAL (50).pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf591795https://repositorio.unal.edu.co/bitstream/unal/86172/4/TRABAJO_FINAL%20%2850%29.pdfa17cf2b1a38121c72632085e1a4ea12cMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/86172/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53THUMBNAILTRABAJO_FINAL (50).pdf.jpgTRABAJO_FINAL (50).pdf.jpgGenerated Thumbnailimage/jpeg4200https://repositorio.unal.edu.co/bitstream/unal/86172/5/TRABAJO_FINAL%20%2850%29.pdf.jpgbe402c351354747753de97e5a3bfaf0fMD55unal/86172oai:repositorio.unal.edu.co:unal/861722024-08-25 23:11:13.695Repositorio Institucional Universidad Nacional de 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