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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 (October 4, 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 (August 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 (October 29, 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 (January 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 variation processes is proposed, allowing in particular a stable DG discretization of hypersingular integral operators. Robustness of the stabilized discretization with respect to various degeneracies in the characteristic triple of the stochastic process is proved. We provide in particular an hp-error analysis of the DG-FEM. Numerical experiments for model equations confirm the theoretical results.

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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 (August 26, 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 (August 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 (December 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 (December 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 (March 11, 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 be used to analyze the thermodynamic limit. The relation to a stochastic representation by an ensemble of interacting random walks is made explicit, and its modifications in presence of a condensate are discussed.

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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 find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method.

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

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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 functions in the same way as the classical algorithm is to the Schur functions. That is, when taking a random word, the algorithm Doob h-transforms the Hamiltonian of the quantum Toda lattice where h are the q-Whittaker functions. Moreover, it can also be applied to model the q-totally asymmetric simple exclusion process introduced in [SW98]. Furthermore, the q-RS algorithm also enjoys a symmetry property analogous to that of the symmetry property of the classical algorithm. This is proved by extending Fomin's growth diagram technique [Fom79, Fom88, Fom94, Fom95], which covers a family of the so-called branching insertion algorithms, including the row insertion proposed in [BP13]. In the second part (Chapters 4, 5) we work with quantum stochastic analysis. First we introduce the basic elements in quantum stochastic analysis, including the quantum probability space, the momentum and position Brownian motions [CH77], and the relation between rotations and angular momenta via the second quantisation, which is generalised to a family of rotation-like operators [HP15a]. Then we discuss a family of unitary quantum causal stochastic double product integrals E, which are expected to be the second quantisation of the continuous limit W of a discrete double product of aforementioned rotation-like operators. In one special case, the operator E is related to the quantum Levy stochastic area, while in another case it is related to the quantum 2-d Bessel process. The explicit formula for the kernel of W is obtained by enumerating linear extensions of partial orderings related to a path model, and the combinatorial aspect is closely related to generalisations of the Catalan numbers and the Dyck paths. Furthermore W is shown to be unitary using integrals of the Bessel functions.

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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
Department of Mathematics
Nathan Albin
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 the stochastic integral. This information will then allow us to introduce stochastic differential equations, along with our overall model. We will conclude with the "optimal estimator", the Kalman Filter, along with an example of its application.

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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 processes. Specifically, particles enter a space according to a space-time Poisson process and are assigned independent and identically distributed attributes. The attributes may determine their movement in the space, and whenever a new particle arrives, it randomly deletes particles from the system according to their attributes. Our main result establishes that spatial Poisson processes are natural temporal limits for a large class of particle systems. Other results include the probability distributions of the sojourn times of particles in the systems, and probabilities of numbers of customers in spatial polling systems without Poisson limits.

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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 adjusted portfolio. (author's abstract)
Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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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 are measurable in time and space using a time discretization scheme with a view towards applications to SPDEs. To achieve this, we require the underlying forward diffusion to have smooth coefficients and we consider convergence in a norm which includes a weighted spatial integral. This combination of smoother forward coefficients and weaker norm allows the use of an equivalence of norms result which is key to our approach. We additionally take a brief look at the approximation of solutions of a class of infinite horizon BDSDEs with a view towards approximating stationary solutions of SPDEs. Whilst we remain agnostic with regards to the implementation of our discretization scheme, our scheme should be amenable to a Monte Carlo simulation based approach. If this is the case, we propose that in addition to being attractive from a performance perspective in higher dimensions, such an approach has a potential advantage when considering measurable coefficients. Specifically, since we only discretize time and effectively rely on simulations of the underlying forward diffusion to explore space, we are potentially less vulnerable to systematically overestimating or underestimating the effects of coefficients with spatial discontinuities than alternative approaches such as finite difference or finite element schemes that do discretize space. Another advantage of the BDSDE approach is that it is possible to derive an upper bound on the error of our method for a fairly broad class of conditions in a single analysis. Furthermore, our conditions seem more general in some respects than is typically considered in the SPDE literature.

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Books on the topic "Discretization of stochastic integrals"

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

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Stochastic integrals. Providence, R.I: AMS Chelsea Pub., 2005.

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

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

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

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

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

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Medvegyev, Peter. Stochastic integration theory. New York: Oxford University Press, 2007.

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

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

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Book chapters on the topic "Discretization of stochastic integrals"

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Dacunha-Castelle, Didier, and Marie Duflo. "Stochastic Integrals." In Probability and Statistics, 331–88. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4870-5_9.

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Kunita, Hiroshi. "Stochastic Integrals." In Stochastic Flows and Jump-Diffusions, 45–75. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3801-4_2.

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Stepanov, Sergey S. "Stochastic Integrals." In Stochastic World, 109–34. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00071-8_5.

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Cuculescu, I., and A. G. Oprea. "Stochastic Integrals." In Noncommutative Probability, 160–233. Dordrecht: 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, 129–54. London: 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, 339–76. New York, NY: 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, 277–305. Boston, MA: 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, 107–39. Cham: 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, 1–24. Cham: 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, 213–37. Cham: 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"

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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 generally recognized that the creation of workable meshes for complex geometric configurations can be difficult, time consuming, and expensive. This discrepancy is further exacerbated when solving solid mechanics problems characterized by a continuous change in the geometry of the domain under analysis. The underlying structures of these methods, which rely on a mesh, are cumbersome in treating moving cracks or mesh distortion. Consequently, the only viable option when applying FEM is to remesh during each discrete step of the model’s evolution. This creates numerical difficulties, even for deterministic analysis, and often leads to degradation in solution accuracy, complexity in computer programming, and a computationally intensive environment. Consequently, there is considerable interest in eliminating or greatly simplifying the meshing task. In recent years, a class of Galerkin-based meshfree or meshless methods have been developed that do not require a structured mesh to discretize the problem, such as the element-free Galerkin method, and the reproducing kernel particle method. These methods employ a moving least-squares approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. Meshless discretization presents significant advantages for modeling fracture propagation. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. Since mesh generation of complex structures can be far more time-consuming and costly than the solution of a discrete set of linear equations, the meshless method provides an attractive alternative to FEM. However, most of the development in meshless methods to date has focused on deterministic problems. Research into probabilistic meshless analysis has not been widespread and is only now gaining attention. Due to inherent uncertainties in loads, material properties and geometry, a probabilistic meshless model is ultimately necessary. Hence, there is considerable interest in developing stochastic meshless methods capable of addressing uncertainties in loads, material properties and geometry, and of predicting the probabilistic response of structures. This paper presents a new stochastic meshless method for predicting probabilistic structural response of cracked structures i.e., mean and variance of the fracture parameters.

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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 presented to evaluate the accuracy of dynamics SIFs calculated by the proposed interaction integrals. Comparisons have been made between the dynamic SIFs predicted by the proposed three interaction integrals and available reference solutions in the literature, generated either analytically or by finite element method using various other fracture integrals or analyses. An excellent agreement is obtained between the results of the proposed interaction integrals and the reference solutions.

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Reports on the topic "Discretization of stochastic integrals"

1

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

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Benhenni, Karim, and Stamatis Cambanis. Sampling Designs for Estimating Integrals of Stochastic rocesses Using Quadratic Mean Derivatives. Fort Belvoir, VA: Defense Technical Information Center, April 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), January 2014. http://dx.doi.org/10.2172/1119920.

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