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Relevant bibliographies by topics / Stochastic integral equations

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Academic literature on the topic 'Stochastic integral equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 February 2023

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Journal articles on the topic "Stochastic integral equations"

1

El-Borai, Mahmoud M., Khairia El-Said El-Nadi, Osama L. Mostafa, and Hamdy M. Ahmed. "Volterra equations with fractional stochastic integrals." Mathematical Problems in Engineering 2004, no. 5 (2004): 453–68. http://dx.doi.org/10.1155/s1024123x04312020.

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Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black-Scholes is considered.

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Mikosch, Thomas, Rimas Norvaiša, and Rimas Norvaisa. "Stochastic Integral Equations without Probability." Bernoulli 6, no. 3 (2000): 401. http://dx.doi.org/10.2307/3318668.

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Malinowski, Marek T. "On multivalued stochastic integral equations driven by semimartingales." Georgian Mathematical Journal 26, no. 3 (2019): 423–36. http://dx.doi.org/10.1515/gmj-2017-0042.

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Abstract We consider multivalued stochastic integral equations driven by semimartingales. Such equations are formulated in two different forms, i.e., using multivalued stochastic up-trajectory and trajectory integrals, which are not equivalent. By the successive approximations method, we show the existence of a unique solution to each equation under a condition much weaker than the Lipschitz one. We indicate that the solutions are stable under small changes of the equation data. The results have immediate implications for solutions to single-valued stochastic integral equations driven by semimartingales.

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Shiralashetti, S. C., and Lata Lamani. "A COMPUTATIONAL METHOD FOR SOLVING STOCHASTIC INTEGRAL EQUATIONS USING HAAR WAVELETS." jnanabha 50, no. 02 (2020): 49–58. http://dx.doi.org/10.58250/jnanabha.2020.50206.

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In this article, we have developed a new technique for solving stochastic integral equations. A new Haar wavelets stochastic operational matrix of integration (HWSOMI) is developed in order to obtain efficient and accurate solution for stochastic integral equations. In the beginning we study the properties of stochastic integrals and Haar wavelets. Convergence and error analysis of Haar wavelet method is presented. Accuracy of the method investigated is justified through some examples.

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Zeghdane, R. "Новый численный метод решения нелинейных стохастических интегральных уравнений". Владикавказский математический журнал, № 4() (22 грудня 2020): 68–86. http://dx.doi.org/10.46698/n8076-2608-1378-r.

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The purpose of this paper is to propose the Chebyshev cardinal functions for solving Volterra stochastic integral equations. The method is based on expanding the required approximate solution as the element of Chebyshev cardinal functions. Though the way, a new operational matrix of integration is derived for the mentioned basis functions. More precisely, the unknown solution is expanded in terms of the Chebyshev cardinal functions including undetermined coefficients. By substituting the mentioned expansion in the original problem, the operational matrix reducing the stochastic integral equation to system of algebraic equations. The convergence and error analysis of the etablished method are investigated in Sobolev space. The method is numerically evaluated by solving test problems caught from the literature by which the computational efficiency of the method is demonstrated. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by other works and it is efficient to use for different problems.

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Malinowski, Marek, and Donal O'Regan. "Bilateral set-valued stochastic integral equations." Filomat 32, no. 9 (2018): 3253–74. http://dx.doi.org/10.2298/fil1809253m.

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We investigate bilateral set-valued stochastic integral equations and these equations combine widening and narrrowing set-valued stochastic integral equations studied in literature. An existence and uniqueness theorem is established using approximate solutions. In addition stability of the solution with respect to small changes of the initial state and coefficients is established, also we provide a result on boundedness of the solution, and an estimate on a distance between the exact solution and the approximate solution is given. Finally some implications for deterministic set-valued integral equations are presented.

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Hu, Yaozhong, and Bernt Øksendal. "Linear Volterra backward stochastic integral equations." Stochastic Processes and their Applications 129, no. 2 (2019): 626–33. http://dx.doi.org/10.1016/j.spa.2018.03.016.

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Ichiba, Tomoyuki, Ioannis Karatzas, Vilmos Prokaj, and Minghan Yan. "Stochastic integral equations for Walsh semimartingales." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, no. 2 (2018): 726–56. http://dx.doi.org/10.1214/16-aihp819.

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Yanishevskyi, V. S., and S. P. Baranovska. "Path integral method for stochastic equations of financial engineering." Mathematical Modeling and Computing 9, no. 1 (2022): 166–77. http://dx.doi.org/10.23939/mmc2022.01.166.

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The integral path method was applied to determine certain stochastic variables which occur in problems of financial engineering. A stochastic variable was defined by a stochastic equation where drift and volatility are functions of a stochastic variable. As a result, for transition probability density, a path integral was built by substituting variables Wiener's path integral (Wiener's measure). For the stochastic equation, Ito rule was applied in order to interpret a stochastic integral. The path integral for transition probability density was also found as a result of the Fokker--Planck equation solution, corresponding to the stochastic equation. It was shown that these two approaches give equivalent results.

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Kolodii, A. M. "Continuous solutions of volterra integral equations with curvilinear stochastic integrals." Journal of Soviet Mathematics 67, no. 4 (1993): 3187–96. http://dx.doi.org/10.1007/bf01261276.

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Dissertations / Theses on the topic "Stochastic integral equations"

1

Mao, Xuerong. "Stochastic integral equations with respect to semimartingales." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/63655/.

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Stochastic integral equations were first developed by mathematicians as a tool for the explicit construction of the paths of diffusion processes for given coefficients of drift and diffusion. Since many physical, engineering, biological as well as social phenomena can be modelled by stochastic integral equations, the theory of stochastic integral equations has become one of the most active fields of mathematical research. This thesis considers stochastic integral equations with respect to semimaningales, which in some sense forms the most general case. This thesis consists of five chapters. In Chapter I we first develop the theory of existence and uniqueness of solutions to stochastic integral equations with respect to semimartingales (SIES) and delay SIES. Chapter II presents the explicit representation of the solutions to linear SIES. Chapter ITIcontains the theory of stochastic stability and boundedness. Chapter IV is for comparison theorems. Chapter V is devoted to the transformation formula which transforms stochastic integrals with respect to continuous local martingales into classical Ito's integrals with respect to Brownian motion. This formula is then applied to study properties of stochastic integrals, SIES and stability.

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Zangeneh, Bijan Z. "Semilinear stochastic evolution equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31117.

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Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation [formula omitted] where • f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measurability conditions. • gs(.) is a uniformly-Lipschitz predictable functional with values in the space of Hilbert-Schmidt operators on H. • Vt is a cadlag adapted process with values in H. • X₀ is a random variable. We obtain existence, uniqueness, boundedness of the solution of this equation. We show the solution of this equation changes continuously when one or all of X₀, f, g, and V are varied. We apply this result to find stationary solutions of certain equations, and to study the associated large deviation principles. Let {Zt,t ∈ R} be an H-valued semimartingale. We prove an Ito-type inequality and a Burkholder-type inequality for stochastic convolution [formula omitted]. These are the main tools for our study of the above stochastic integral equation.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate

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Xie, Shuguang School of Mathematics UNSW. "Stochastic heat equations with memory in infinite dimensional spaces." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/24257.

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This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

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Lam, Wai Hung. "Integral functional methods in stochastic filtering problems." HKBU Institutional Repository, 1992. https://repository.hkbu.edu.hk/etd_ra/17.

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Brown, Martin Lloyd. "Stochastic process approximation method with application to random volterra integral equations." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/29222.

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Sipiläinen, Eeva-Maria. "Pathwise view on solutions of stochastic differential equations." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/8202.

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The Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise functions, large enough to include almost all Brownian paths. The algebraic structure of iterated path integrals for smooth paths leads to a formal definition of a solution for a differential equation in terms of generalized path integrals for more general noises. This suggests a way of constructing solutions to differential equations in a large class of paths as limits of operators. The concept of the driving noise is extended to include the generalized path integrals of the noise. Less stringent conditions on the Holder continuity of the path can be compensated by giving more of its iterated integrals. Sufficient conditions for the solution to exist are proved in some special cases, and it is proved that almost all paths of Brownian motion as well as some other stochastic processes can be included in the theory.

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Sockell, Michael Elliot. "Similarity solutions of stochastic nonlinear parabolic equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49898.

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A novel statistical technique introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in terms of the moments of the wave function. In the latter, all even-order moments are computed exactly, whereas the odd-order moments are solved asymptotically. Lastly, it is shown that this statistical technique is isomorphic to mappings of nonconstant coefficient partial differential equations to constant coefficient equations. A generalization of this mapping and its inherent restrictions are discussed.<br>Ph. D.<br>incomplete_metadata

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Jin, Chao. "Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256468.

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Hamaguchi, Yushi. "Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263434.

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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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Books on the topic "Stochastic integral equations"

1

Mao, Xuerong. Stochastic integral equations with respect to semimartingales. typescript, 1989.

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Hromadka, Theodore V., and Robert J. Whitley. Stochastic Integral Equations and Rainfall-Runoff Models. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-49309-6.

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Hromadka, Theodore V. Stochastic integral equations and rainfall-runoff models. Springer-Verlag, 1989.

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Hromadka, Theodore V. Stochastic Integral Equations and Rainfall-Runoff Models. Springer Berlin Heidelberg, 1989.

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Lévy processes and stochastic calculus. 2nd ed. Cambridge University Press, 2009.

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Wędrychowicz, Stanisław. Compactness conditions for nonlinear stochastic differential and integral equations. Wydawn. Uniwersytetu Jagiellońskiego, 2001.

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1963-, Zhang Tusheng, and Zhao Huaizhong 1964-, eds. The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations. American Mathematical Society, 2008.

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8

Assing, Sigurd. Continuous strong Markov processes in dimension one: A stochastic calculus approach. Springer, 1998.

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Toka, Diagana, and SpringerLink (Online service), eds. Almost Periodic Stochastic Processes. Springer Science+Business Media, LLC, 2011.

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Michael, Evans. An algorithm for the approximation of integrals with exact error bounds. University of Toronto, Dept. of Statistics, 1997.

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Book chapters on the topic "Stochastic integral equations"

1

O’Regan, Donal, and Maria Meehan. "Stochastic Integral Equations." In Existence Theory for Nonlinear Integral and Integrodifferential Equations. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-4992-1_11.

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Haba, Zbigniew. "Stochastic differential equations." In Feynman Integral and Random Dynamics in Quantum Physics. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4716-3_3.

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Atangana, Abdon, and Seda İgret Araz. "Fractional Differential and Integral Operators." In Fractional Stochastic Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6_2.

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Desch, Wolfgang, and Stig-Olof Londen. "On a Stochastic Parabolic Integral Equation." In Functional Analysis and Evolution Equations. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7794-6_10.

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Mandrekar, Vidyadhar, and Barbara Rüdiger. "Stochastic Integral Equations in Banach Spaces." In Stochastic Integration in Banach Spaces. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12853-5_4.

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Haba, Zbigniew. "Feynman integral and stochastic differential equations." In Feynman Integral and Random Dynamics in Quantum Physics. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4716-3_6.

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Alòs, Elisa, and David Nualart. "A Maximal Inequality for the Skorohod Integral." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_18.

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Hromadka, Theodore V., and Robert J. Whitley. "Using the Stochastic Integral Equation Method." In Stochastic Integral Equations and Rainfall-Runoff Models. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-49309-6_6.

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Malinowski, Marek T., and Mariusz Michta. "Fuzzy Stochastic Integral Equations Driven by Martingales." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22833-9_17.

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Shigeyoshi, Ogawa. "Stochastic integral equations for the random fields." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0100866.

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Conference papers on the topic "Stochastic integral equations"

1

Todorov, Venelin, Ivan Dimov, Stefka Fidanova, and Rayna Georgieva. "Optimized stochastic approach for integral equations." In 16th Conference on Computer Science and Intelligence Systems. IEEE, 2021. http://dx.doi.org/10.15439/2021f54.

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Ferreyra, Guillermo. "Stochastic integral equations controlled by collor processes." In 26th IEEE Conference on Decision and Control. IEEE, 1987. http://dx.doi.org/10.1109/cdc.1987.272494.

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Насыров, Фарит. "Inverse stochastic differential equations with symmetric integral." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh2t-2021-10-06.25.

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Jasim, Abdulghafoor, and Ali Asmael. "Studying Some Stochastic Differential Equations with trigonometric terms with Application." In 3rd International Conference of Mathematics and its Applications. Salahaddin University-Erbil, 2020. http://dx.doi.org/10.31972/ticma22.13.

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In this paper we look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.

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CHEN, SHUPING, and JIONGMIN YONG. "A LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM FOR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS." In Control Theory and Related Topics - In Memory of Professor Xunjing Li. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812790552_0005.

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Lv, Wen, and Cunxia Liu. "Backward stochastic Volterra integral equations driven by a Lévy process." In 2010 2nd International Conference on Education Technology and Computer (ICETC). IEEE, 2010. http://dx.doi.org/10.1109/icetc.2010.5529291.

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de la Cruz, Hugo, C. H. Olivera, and J. P. Zubelli. "On the numerical integration of a random integral equation arising in the simulation of stochastic transport equations." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825986.

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Michielsen, B. L., O. O. Sy, and M. C. van Beurden. "Estimates in first order approximations to electromagnetic boundary integral equations on stochastic surfaces." In 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2013. http://dx.doi.org/10.1109/iceaa.2013.6632419.

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Travkin, V. S., K. Hu, and I. Catton. "Statistics of Mathematical Two-Scale Closure of Momentum, Heat and Charge Transport Problems With Stochastic Orientation of Porous Medium Capillaries." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24157.

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Abstract The history of stochastic capillary porous media transport problem treatments almost corresponds to the history of porous media transport developments. Volume Averaging Theory (VAT), shown to be an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in capillary porous media. VAT based modeling of pore level transport in stochastic capillaries results in two sets of scale governing equations. This work shows how the two scale equations could be solved and how the results could be presented using statistical analysis. We demonstrate that stochastic orientation and diameter of the pores are incorporated in the upper scale simulation procedures. We are treating this problem with conditions of Bi for each pore is in a range when Bi ≳ 0.1 which allows even greater distinction in assessing an each additional differential, integral, or integral-differential term in the VAT equations.

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Agrawal, Om P. "Stochastic Analysis of a Fractionally Damped Beam." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21365.

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Abstract This paper presents a general analytical technique for stochastic analysis of a continuous beam whose damping characteristic is described using a fractional derivative model. In this formulation, the normal-mode approach is used to reduce the differential equation of a fractionally damped continuous beam into a set of infinite equations each of which describes the dynamics of a fractionally damped spring-mass-damper system. A Laplace transform technique is used to obtain the fractional Green’s function and a Duhamel integral type expression for the system’s response. The response expression contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for White noise. The approach can be extended to all those systems for which the existence of normal modes is guaranteed.

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