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Relevant bibliographies by topics / Discretization of stochastic integrals

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Academic literature on the topic 'Discretization of stochastic integrals'

Author: Grafiati

Published: 16 December 2023

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Journal articles on the topic "Discretization of stochastic integrals"

1

Fukasawa, Masaaki. "Efficient discretization of stochastic integrals." Finance and Stochastics 18, no. 1 (2013): 175–208. http://dx.doi.org/10.1007/s00780-013-0215-6.

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Fukasawa, Masaaki. "Discretization error of stochastic integrals." Annals of Applied Probability 21, no. 4 (2011): 1436–65. http://dx.doi.org/10.1214/10-aap730.

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Gobet, Emmanuel, and Uladzislau Stazhynski. "Model-adaptive optimal discretization of stochastic integrals." Stochastics 91, no. 3 (2018): 321–51. http://dx.doi.org/10.1080/17442508.2018.1539087.

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MARAZZINA, DANIELE, OLEG REICHMANN, and CHRISTOPH SCHWAB. "hp-DGFEM FOR KOLMOGOROV–FOKKER–PLANCK EQUATIONS OF MULTIVARIATE LÉVY PROCESSES." Mathematical Models and Methods in Applied Sciences 22, no. 01 (2012): 1150005. http://dx.doi.org/10.1142/s0218202512005897.

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We analyze the discretization of nonlocal degenerate integrodifferential equations arising as so-called forward equations for jump-diffusion processes. Such equations arise in option pricing problems when the stochastic dynamics of the markets is modeled by Lévy driven stochastic volatility models. Well-posedness of the arising equations is addressed. We develop and analyze stable discretization schemes, in particular the discontinuous Galerkin Finite Element Methods (DG-FEM). In the DG-FEM, a new regularization of hypersingular integrals in the Dirichlet form of the pure jump part of infinite

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Zhou, Li-kai, and Zhong-gen Su. "Discretization error of irregular sampling approximations of stochastic integrals." Applied Mathematics-A Journal of Chinese Universities 31, no. 3 (2016): 296–306. http://dx.doi.org/10.1007/s11766-016-3426-8.

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Gobet, Emmanuel, and Uladzislau Stazhynski. "Optimal discretization of stochastic integrals driven by general Brownian semimartingale." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, no. 3 (2018): 1556–82. http://dx.doi.org/10.1214/17-aihp848.

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Kloeden, P. E., E. Platen, H. Schurz, and M. Sørensen. "On effects of discretization on estimators of drift parameters for diffusion processes." Journal of Applied Probability 33, no. 4 (1996): 1061–76. http://dx.doi.org/10.2307/3214986.

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In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

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Kloeden, P. E., E. Platen, H. Schurz, and M. Sørensen. "On effects of discretization on estimators of drift parameters for diffusion processes." Journal of Applied Probability 33, no. 04 (1996): 1061–76. http://dx.doi.org/10.1017/s0021900200100488.

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In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

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Salmhofer, Manfred. "Functional Integral and Stochastic Representations for Ensembles of Identical Bosons on a Lattice." Communications in Mathematical Physics 385, no. 2 (2021): 1163–211. http://dx.doi.org/10.1007/s00220-021-04010-4.

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AbstractRegularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is proven for various discretized actions. The focus is on the integral representation for the partition function and expectation values in the canonical ensemble. The connection to the grand-canonical integral is exhibited and some important differences are discussed. Uniform bounds for covariances are proven, which simplify the analysis of the time-continuum limit and can also b

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Tynda, Aleksandr, Samad Noeiaghdam, and Denis Sidorov. "Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind." Bulletin of Irkutsk State University. Series Mathematics 39 (2022): 62–79. http://dx.doi.org/10.26516/1997-7670.2022.39.62.

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The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to f

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Dissertations / Theses on the topic "Discretization of stochastic integrals"

1

Pokalyuk, Stanislav [Verfasser], and Christian [Akademischer Betreuer] Bender. "Discretization of backward stochastic Volterra integral equations / Stanislav Pokalyuk. Betreuer: Christian Bender." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2012. http://d-nb.info/1052338488/34.

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Pei, Yuchen. "Robinson-Schensted algorithms and quantum stochastic double product integrals." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/74169/.

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This thesis is divided into two parts. In the first part (Chapters 1, 2, 3) various Robinson-Schensted (RS) algorithms are discussed. An introduction to the classical RS algorithm is presented, including the symmetry property, and the result of the algorithm Doob h-transforming the kernel from the Pieri rule of Schur functions h when taking a random word [O'C03a]. This is followed by the extension to a q-weighted version that has a branching structure, which can be alternatively viewed as a randomisation of the classical algorithm. The q-weighted RS algorithm is related to the q-Whittaker func

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Brooks, Martin George. "Quantum spectral stochastic integrals and levy flows in Fock space." Thesis, Nottingham Trent University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266915.

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SONG, YUKUN SONG. "Stochastic Integrals with Respect to Tempered $\alpha$-Stable Levy Process." Case Western Reserve University School of Graduate Studies / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=case1501506513936836.

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Gross, Joshua. "An exploration of stochastic models." Kansas State University, 2014. http://hdl.handle.net/2097/17656.

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Master of Science<br>Department of Mathematics<br>Nathan Albin<br>The term stochastic is defined as having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely. A stochastic model attempts to estimate outcomes while allowing a random variation in one or more inputs over time. These models are used across a number of fields from gene expression in biology, to stock, asset, and insurance analysis in finance. In this thesis, we will build up the basic probability theory required to make an ``optimal estimate", as well as construct t

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Jones, Matthew O. "Spatial Service Systems Modelled as Stochastic Integrals of Marked Point Processes." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7174.

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We characterize the equilibrium behavior of a class of stochastic particle systems, where particles (representing customers, jobs, animals, molecules, etc.) enter a space randomly through time, interact, and eventually leave. The results are useful for analyzing the dynamics of randomly evolving systems including spatial service systems, species populations, and chemical reactions. Such models with interactions arise in the study of species competitions and systems where customers compete for service (such as wireless networks). The models we develop are space-time measure-valued Markov proc

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Kuwada, Kazumasa. "On large deviations for current-valued processes induced from stochastic line integrals." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/147585.

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Leoff, Elisabeth [Verfasser]. "Stochastic Filtering in Regime-Switching Models: Econometric Properties, Discretization and Convergence / Elisabeth Leoff." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126297348/34.

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Geiss, Stefan. "On quantitative approximation of stochastic integrals with respect to the geometric Brownian motion." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1774/1/document.pdf.

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We approximate stochastic integrals with respect to the geometric Brownian motion by stochastic integrals over discretized integrands, where deterministic, but not necessarily equidistant, time nets are used. This corresponds to the approximation of a continuously adjusted portfolio by a discretely adjusted one. We compute the approximation orders of European Options in the Black Scholes model with respect to L_2 and the approximation order of the standard European-Call and Put Option with respect to an appropriate BMO space, which gives information about the cost process of the discretely adj

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Yeadon, Cyrus. "Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/20643.

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It has been shown that backward doubly stochastic differential equations (BDSDEs) provide a probabilistic representation for a certain class of nonlinear parabolic stochastic partial differential equations (SPDEs). It has also been shown that the solution of a BDSDE with Lipschitz coefficients can be approximated by first discretizing time and then calculating a sequence of conditional expectations. Given fixed points in time and space, this approximation has been shown to converge in mean square. In this thesis, we investigate the approximation of solutions of BDSDEs with coefficients that ar

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Books on the topic "Discretization of stochastic integrals"

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von Weizsäcker, Heinrich, and Gerhard Winkler. Stochastic Integrals. Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-663-13923-2.

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Stochastic integrals. AMS Chelsea Pub., 2005.

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E, Protter Philip, and SpringerLink (Online service), eds. Discretization of Processes. Springer-Verlag Berlin Heidelberg, 2012.

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Weizsäcker, Heinrich Von. Stochastic integrals: An introduction. F. Vieweg, 1990.

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5

Instytut Matematyczny (Polska Akademia Nauk), ed. Bilinear random integrals. Państwowe Wydawn. Naukowe, 1987.

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Kisielewicz, Michał. Set-Valued Stochastic Integrals and Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40329-4.

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Bell, Denis. The Malliavin calculus. Longman Scientific and Technical, 1987.

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Medvegyev, Peter. Stochastic integration theory. Oxford University Press, 2007.

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9

Kuznet︠s︡ov, D. F. Strong approximation of multiple Ito and Stratonovich stochastic integrals: Multple Fourier series approach. Politechnical University Publishing House, 2011.

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10

Koning, A. J. Stochastic integrals and goodness-of-fit tests. Centrum voor Wiskunde en Informatica, 1993.

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Book chapters on the topic "Discretization of stochastic integrals"

1

Dacunha-Castelle, Didier, and Marie Duflo. "Stochastic Integrals." In Probability and Statistics. Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4870-5_9.

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2

Kunita, Hiroshi. "Stochastic Integrals." In Stochastic Flows and Jump-Diffusions. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3801-4_2.

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3

Stepanov, Sergey S. "Stochastic Integrals." In Stochastic World. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00071-8_5.

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4

Cuculescu, I., and A. G. Oprea. "Stochastic Integrals." In Noncommutative Probability. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8374-9_5.

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Grigoriu, Mircea. "Stochastic Integrals." In Springer Series in Reliability Engineering. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2327-9_4.

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Glasserman, Paul. "Discretization Methods." In Stochastic Modelling and Applied Probability. Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-21617-1_6.

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Kwapień, Stanisław, and Wojbor A. Woyczyński. "Multiple Stochastic Integrals." In Random Series and Stochastic Integrals: Single and Multiple. Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0425-1_11.

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Kisielewicz, Michał. "Aumann Stochastic Integrals." In Set-Valued Stochastic Integrals and Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40329-4_4.

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Tudor, Ciprian. "Multiple Stochastic Integrals." In SpringerBriefs in Probability and Mathematical Statistics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33772-7_1.

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Hassler, Uwe. "Ito Integrals." In Stochastic Processes and Calculus. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-23428-1_10.

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Conference papers on the topic "Discretization of stochastic integrals"

1

Rao, B. N., C. O. Arun, and M. S. Siva Kumar. "Stochastic Meshfree Method for Computational Fracture Mechanics." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26794.

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In the stochastic mechanics community, the need to account for uncertainty has long been recognized as key to achieving the reliable design of structural and mechanical systems. It is generally agreed that advanced computational tools must be employed to provide the necessary computational framework for describing structural response. A currently popular method is the stochastic finite element method (SFEM), which integrates probability theory with the standard finite element method (FEM). However, SFEM requires a structured mesh to perform the underlying finite element analysis. It is general

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Joseph Spring, William, Timothy Ralph, and Ping Koy Lam. "Multidimensional Quantum Stochastic Integrals." In QUANTUM COMMUNICATION, MEASUREMENT AND COMPUTING (QCMC): The Tenth International Conference. AIP, 2011. http://dx.doi.org/10.1063/1.3630154.

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Zhang, Jinping. "Interval-valued Stochastic Processes and Stochastic Integrals." In Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icicic.2007.365.

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Carpio-Bernido, M. Victoria, Christopher C. Bernido, Christopher C. Bernido, and M. Victoria Carpio-Bernido. "White Noise Path Integrals in Stochastic Neurodynamics." In STOCHASTIC AND QUANTUM DYNAMICS OF BIOMOLECULAR SYSTEMS: Proceedings of the 5th Jagna International Workshop. AIP, 2008. http://dx.doi.org/10.1063/1.2956763.

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HUDSON, R. L. "MULTIPLICATIVE PROPERTIES OF DOUBLE STOCHASTIC PRODUCT INTEGRALS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704290_0010.

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SPRING, W. J., and I. F. WILDE. "QUASI-FREE FERMION PLANAR QUANTUM STOCHASTIC INTEGRALS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704290_0017.

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SPRING, W. J. "QUASI-FREE STOCHASTIC INTEGRALS AND MARTINGALE REPRESENTATION." In Proceedings of the 28th Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812835277_0019.

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Budak, Hüseyin, Mehmet Zeki Sarikaya, and Zoubir Dahmani. "Chebyshev type inequalities for generalized stochastic fractional integrals." In II. INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2017. Author(s), 2017. http://dx.doi.org/10.1063/1.4981655.

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Prasanth, Ravi K. "Analysis of stochastic hybrid systems using path integrals." In AeroSense 2003, edited by Ivan Kadar. SPIE, 2003. http://dx.doi.org/10.1117/12.487038.

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Meenakshi, T., and B. N. Rao. "On Comparison of Various Formulations for Evaluation of Dynamic SIFs in FGMs." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93755.

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This paper presents three interaction integrals for calculating dynamic stress-intensity factors (SIFs) for a crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves the finite element discretization, where the material properties are smooth functions of spatial co-ordinates and three interaction integrals for mixed-mode dynamic fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as meshless method, boundary element method, and others. Numerical examples involving mixed-mode problems are presente

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Reports on the topic "Discretization of stochastic integrals"

1

Hudson, W. N. Stochastic Integrals and Processes with Independent Increments. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada158939.

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2

Benhenni, Karim, and Stamatis Cambanis. Sampling Designs for Estimating Integrals of Stochastic rocesses Using Quadratic Mean Derivatives. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada225961.

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Chen, X., J. M. Connors, and C. H. Tong. A flexible method to calculate the distributions of discretization errors in operator-split codes with stochastic noise in problem data. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1119920.

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