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Relevant bibliographies by topics / Forward Backward Stochastic Differential Equations (FBSDE)

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Academic literature on the topic 'Forward Backward Stochastic Differential Equations (FBSDE)'

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Published: 1 February 2025

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Journal articles on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

1

Zhang, Kevin, Junhao Zhu, Dehan Kong, and Zhaolei Zhang. "Modeling single cell trajectory using forward-backward stochastic differential equations." PLOS Computational Biology 20, no. 4 (2024): e1012015. http://dx.doi.org/10.1371/journal.pcbi.1012015.

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Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible

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Takahashi, Akihiko, and Toshihiro Yamada. "An asymptotic expansion of forward-backward SDEs with a perturbed driver." International Journal of Financial Engineering 02, no. 02 (2015): 1550020. http://dx.doi.org/10.1142/s2424786315500206.

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Motivated by nonlinear pricing in finance, this paper presents a mathematical validity of an asymptotic expansion scheme for a system of forward-backward stochastic differential equations (FBSDEs) in terms of a perturbed driver in the BSDE and a small diffusion in the FSDE. In particular, we represent the coefficients of the expansion of the FBSDE up to an arbitrary order, and obtain the error estimate of the expansion with respect to the driver and the small noise perturbation.

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Yang, Jie, and Weidong Zhao. "Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation." East Asian Journal on Applied Mathematics 5, no. 4 (2015): 387–404. http://dx.doi.org/10.4208/eajam.280515.211015a.

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AbstractConvergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FB-SDEs) that arises in finance and stochastic control. The corresponding k-step scheme admits a k-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

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Geiss, Christel, Céline Labart, and Antti Luoto. "Mean square rate of convergence for random walk approximation of forward-backward SDEs." Advances in Applied Probability 52, no. 3 (2020): 735–71. http://dx.doi.org/10.1017/apr.2020.17.

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AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the part

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Ji, Shaolin, Chuanfeng Sun, and Qingmeng Wei. "The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/958920.

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This paper is devoted to a stochastic differential game (SDG) of decoupled functional forward-backward stochastic differential equation (FBSDE). For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs). Applying the Girsanov transformation method introduced by Buckdahn and Li (2008), the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations to the path-dependent ones. By establishing the dy

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Song, Yunquan. "Terminal-Dependent Statistical Inference for the FBSDEs Models." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/365240.

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The original stochastic differential equations (OSDEs) and forward-backward stochastic differential equations (FBSDEs) are often used to model complex dynamic process that arise in financial, ecological, and many other areas. The main difference between OSDEs and FBSDEs is that the latter is designed to depend on a terminal condition, which is a key factor in some financial and ecological circumstances. It is interesting but challenging to estimate FBSDE parameters from noisy data and the terminal condition. However, to the best of our knowledge, the terminal-dependent statistical inference fo

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DOS REIS, GONÇALO, and RICARDO J. N. DOS REIS. "A NOTE ON COMONOTONICITY AND POSITIVITY OF THE CONTROL COMPONENTS OF DECOUPLED QUADRATIC FBSDE." Stochastics and Dynamics 13, no. 04 (2013): 1350005. http://dx.doi.org/10.1142/s0219493713500056.

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In this note we are concerned with the solution of Forward–Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a by-product one obtains conditions that allow establishing the positivity of the control process.

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Wang, Mingcan, and Xiangjun Wang. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations." Mathematics 12, no. 7 (2024): 1081. http://dx.doi.org/10.3390/math12071081.

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The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high-dimensional cases, has stagnated. The development of deep learning provides ideas for its high-dimensional solution. In this paper, our focus lies on the fully coupled forward–backward stochastic differential equation. We design a neural network structure tailored to the characteristics of the equation and develop a hybrid BiGRU model for solvi

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Wu, Zhen. "Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration." Journal of the Australian Mathematical Society 74, no. 2 (2003): 249–66. http://dx.doi.org/10.1017/s1446788700003281.

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AbstractWe first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.

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Wei, Qingmeng, Jiongmin Yong, and Zhiyong Yu. "Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 17. http://dx.doi.org/10.1051/cocv/2018013.

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An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable random variables. The main motivation of our study is linear quadratic (LQ, for short) optimal control problems for mean-field stochastic differential equations. Open-loop solvability of the problem is characterized as the solvability of a system of linear coupled forward-backward stochastic differential equations (FBSDE, for short) with operato

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Dissertations / Theses on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Fromm, Alexander. "Theory and applications of decoupling fields for forward-backward stochastic differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2015. http://dx.doi.org/10.18452/17115.

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Diese Arbeit beschäftigt sich mit der Theorie der sogenannten stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDE), welche als ein stochastisches Anologon und in gewisser Weise als eine Verallgemeinerung von parabolischen quasi-linearen partiellen Differentialgleichungen betrachtet werden können. Die Dissertation besteht aus zwei Teilen: In dem ersten entwicklen wir die Theorie der sogenannten Entkopplungsfelder für allgemeine mehrdimensionale stark gekoppelte FBSDE. Diese Theorie besteht aus Existenz- sowie Eindeutigkeitsresultaten basierend auf dem Konzept des maximalen Interva

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Wang, Xince. "Quasilinear PDEs and forward-backward stochastic differential equations." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17383.

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In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs.

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Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi q

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Manai, Arij. "Some contributions to backward stochastic differential equations and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1022.

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Cette thèse est consacrée à l'étude des équations différentielles stochastiques rétrogrades (EDSR) et leurs applications. Dans le chapitre 1, on étudie le problème de maximisation de l'utilité de la richesse terminale où le prix de l'actif peut être discontinue sous des contraintes sur les stratégies de l'agent. Nous nous concentrons sur l'EDSR dont la solution représente l'utilité maximale, ce qui permet de transférer des résultats sur les EDSR quadratiques, en particulier les résultats de stabilité, au problème de maximisation d'utilité. Dans le chapitre 2, nous considèrons le problème de va

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Salhi, Rym. "Contributions to quadratic backward stochastic differential equations with jumps and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1023.

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Cette thèse porte sur l'étude des équations différentielles stochastiques rétrogrades (EDSR) avec sauts et leurs applications.Dans le chapitre 1, nous étudions une classe d'EDSR lorsque le bruit provient d'un mouvement Brownien et d'une mesure aléatoire de saut indépendante à activité infinie. Plus précisément, nous traitons le cas où le générateur est à croissance quadratique et la condition terminale est non bornée. L'existence et l'unicité de la solution sont prouvées en combinant à la fois la procédure d'approximation monotone et une approche progressive. Cette méthode permet de résoudre l

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Fromm, Alexander [Verfasser], Peter [Akademischer Betreuer] Imkeller, Stefan [Akademischer Betreuer] Ankirchner, and Anthony [Akademischer Betreuer] Réveillac. "Theory and applications of decoupling fields for forward-backward stochastic differential equations / Alexander Fromm. Gutachter: Peter Imkeller ; Stefan Ankirchner ; Anthony Réveillac." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2015. http://d-nb.info/1065723083/34.

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Ouknine, Anas. "Μοdèles affines généralisées et symétries d'équatiοns aux dérivés partielles". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMR085.

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Cette thèse se consacre à étudier les symétries de Lie d'une classe particulière d'équations différentielles partielles (EDP), désignée sous le nom d'équation de Kolmogorov rétrograde. Cette équation joue un rôle essentiel dans le cadre des modèles financiers, notamment en lien avec le modèle de Longstaff-Schwartz, qui est largement utilisé pour la valorisation des options et des produits dérivés.Dans un contexte plus générale, notre étude s'oriente vers l'analyse des symétries de Lie de l'équation de Kolmogorov rétrograde, en introduisant un terme non linéaire. Cette généralisation est signif

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Mtiraoui, Ahmed. "I. Etude des EDDSRs surlinéaires II. Contrôle des EDSPRs couplées." Thesis, Toulon, 2016. http://www.theses.fr/2016TOUL0010/document.

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Cette thèse aborde deux sujets de recherches, le premier est sur l’existence et l’unicité des solutions des Équations Différentielles Doublement Stochastiques Rétrogrades (EDDSRs) et les Équations aux Dérivées partielles Stochastiques (EDPSs) multidimensionnelles à croissance surlinéaire. Le deuxième établit l’existence d’un contrôle optimal strict pour un système controlé dirigé par des équations différentielles stochastiques progressives rétrogrades (EDSPRs) couplées dans deux cas de diffusions dégénérée et non dégénérée.• Existence et unicité des solutions des EDDSRs multidimensionnels :Nou

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Wu, Yue. "Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15991.

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In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a sol

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Zhang, Liangliang. "Essays on numerical solutions to forward-backward stochastic differential equations and their applications in finance." Thesis, 2017. https://hdl.handle.net/2144/26430.

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In this thesis, we provide convergent numerical solutions to non-linear forward-BSDEs (Backward Stochastic Differential Equations). Applications in mathematical finance, financial economics and financial econometrics are discussed. Numerical examples show the effectiveness of our methods.

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Books on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Ma, Jin, and Jiongmin Yong. Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6.

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Ma, Jin. Forward-backward stochastic differential equations and their applications. Springer, 1999.

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Forward-Backward Stochastic Differential Equations and Their Applications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0092524.

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Yong, Jiongmin, and Jin Ma. Forward-Backward Stochastic Differential Equations and Their Applications. Springer London, Limited, 2007.

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Chassagneux, Jean-François, Hinesh Chotai, and Mirabelle Muûls. A Forward-Backward SDEs Approach to Pricing in Carbon Markets. Springer, 2017.

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Ma, Jin, and Jiongmin Yong. Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics). Springer, 2007.

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Book chapters on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Zhang, Jianfeng. "Forward-Backward SDEs." In Backward Stochastic Differential Equations. Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7256-2_8.

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Delong, Łukasz. "Forward-Backward Stochastic Differential Equations." In EAA Series. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5331-3_4.

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Chassagneux, Jean-François, Hinesh Chotai, and Mirabelle Muûls. "Introduction to Forward-Backward Stochastic Differential Equations." In A Forward-Backward SDEs Approach to Pricing in Carbon Markets. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63115-8_2.

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Ma, Jin, and Tim Zajic. "Rough Asymptotics of Forward-Backward Stochastic Differential Equations." In Control of Distributed Parameter and Stochastic Systems. Springer US, 1999. http://dx.doi.org/10.1007/978-0-387-35359-3_29.

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Kebiri, Omar, Lara Neureither, and Carsten Hartmann. "Adaptive Importance Sampling with Forward-Backward Stochastic Differential Equations." In Stochastic Dynamics Out of Equilibrium. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15096-9_7.

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Kohlmann, Michael. "Reflected Forward Backward Stochastic Differential Equations and Contingent Claims." In Control of Distributed Parameter and Stochastic Systems. Springer US, 1999. http://dx.doi.org/10.1007/978-0-387-35359-3_27.

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Kim, Jin Won, and Sebastian Reich. "On Forward–Backward SDE Approaches to Conditional Estimation." In Mathematics of Planet Earth. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70660-8_6.

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AbstractIn this chapter, we investigate the representation of conditional expectation values for partially observed diffusion processes in terms of appropriate estimators. The work of Kalman and Bucy has established a duality between filtering and estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an optimization problem constrained by a backward stochastic partial differential equation. Here we revisit this problem from the perspective of appropriate forward-backward stochastic differential equations. Our approach sheds new light on the conditional estimation problem and provides a unifying perspective. It is also demonstrated that certain formulations of the estimation problem lead to deterministic formulations similar to the linear Gaussian case as originally investigated by Kalman and Bucy. Finally, we discuss an application of the proposed formulation to optimal control problem on partially observed diffusion processes.

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Jiménez-Pastor, A., K. G. Larsen, M. Tribastone, and M. Tschaikowski. "Forward and Backward Constrained Bisimulations for Quantum Circuits." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57249-4_17.

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AbstractEfficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation, an established class of techniques that has been proven successful for (classic) stochastic and deterministic systems such as Markov chains and ordinary differential equations. Forward constrained bisimulation yields a lower-dimensional model which exactly preserves quantum measurements projected on a linear subspace of interest. Backward constrained bisimulation gives a reduction that is valid on a subspace containing the circuit input, from which the circuit result can be fully recovered. We provide an algorithm to compute the constraint bisimulations yielding coarsest reductions in both cases, using a duality result relating the two notions. As applications, we provide theoretical bounds on the size of the reduced state space for well-known quantum algorithms for search, optimization, and factorization. Using a prototype implementation, we report significant reductions on a set of benchmarks. Furthermore, we show that constraint bisimulation complements state-of-the-art methods for the simulation of quantum circuits based on decision diagrams.

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"FBSDEs with Reflections." In Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6_7.

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"Applications of FBSDEs." In Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6_8.

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Conference papers on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Exarchos, Ioannis, and Evangelos A. Theodorou. "Learning optimal control via forward and backward stochastic differential equations." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7525237.

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Exarchos, Ioannis, Evangelos A. Theodorou, and Panagiotis Tsiotras. "Game-theoretic and risk-sensitive stochastic optimal control via forward and backward stochastic differential equations." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799215.

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Shanshan, Zuo, and Min Hui. "Optimal control problems of mean-field forward-backward stochastic differential equations with partial information." In 2013 25th Chinese Control and Decision Conference (CCDC). IEEE, 2013. http://dx.doi.org/10.1109/ccdc.2013.6561841.

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Ashok Naarayan, Aadhithya, and Panos Parpas. "Stable Multilevel Deep Neural Networks for Option Pricing and xVAs Using Forward-Backward Stochastic Differential Equations." In ICAIF '24: 5th ACM International Conference on AI in Finance. ACM, 2024. http://dx.doi.org/10.1145/3677052.3698598.

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Hawkins, Kelsey P., Ali Pakniyat, and Panagiotis Tsiotras. "On the Time Discretization of the Feynman-Kac Forward-Backward Stochastic Differential Equations for Value Function Approximation." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683583.

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