Relevant bibliographies by topics / Stochastic convergence

Academic literature on the topic 'Stochastic convergence'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Stochastic convergence"

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Abdulghafor, Rawad, Sherzod Turaev, Akram Zeki, and Adamu Abubaker. "Nonlinear Convergence Algorithm: Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems." Journal of Artificial Intelligence and Soft Computing Research 8, no. 1 (January 1, 2018): 49–61. http://dx.doi.org/10.1515/jaiscr-2018-0003.

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Abstract This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem (CP) of discrete-time for multi-agent systems (MAS) on n-dimensional simplex. The first part undertakes systematic review of consensus problems. Convergence was generated via extreme doubly stochastic quadratic operators (EDSQOs) in the other part. However, this work was able to formulate convergence algorithms from doubly stochastic matrices, majorization theory, graph theory and stochastic analysis. We develop two algorithms: 1) the nonlinear algorithm of extreme doubly stochastic quadratic operator (NLAEDSQO) to generate all the convergent EDSQOs and 2) the nonlinear convergence algorithm (NLCA) of EDSQOs to investigate the optimal consensus for MAS. Experimental evaluation on convergent of EDSQOs yielded an optimal consensus for MAS. Comparative analysis with the convergence of EDSQOs and DeGroot model were carried out. The comparison was based on the complexity of operators, number of iterations to converge and the time required for convergences. This research proposed algorithm on convergence which is faster than the DeGroot linear model.
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Sánchez-López, Borja, and Jesus Cerquides. "On the Convergence of Stochastic Process Convergence Proofs." Mathematics 9, no. 13 (June 23, 2021): 1470. http://dx.doi.org/10.3390/math9131470.

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Convergence of a stochastic process is an intrinsic property quite relevant for its successful practical for example for the function optimization problem. Lyapunov functions are widely used as tools to prove convergence of optimization procedures. However, identifying a Lyapunov function for a specific stochastic process is a difficult and creative task. This work aims to provide a geometric explanation to convergence results and to state and identify conditions for the convergence of not exclusively optimization methods but any stochastic process. Basically, we relate the expected directions set of a stochastic process with the half-space of a conservative vector field, concepts defined along the text. After some reasonable conditions, it is possible to assure convergence when the expected direction resembles enough to some vector field. We translate two existent and useful convergence results into convergence of processes that resemble to particular conservative vector fields. This geometric point of view could make it easier to identify Lyapunov functions for new stochastic processes which we would like to prove its convergence.
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Hu, Peng, and Chengming Huang. "The StochasticΘ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/583930.

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The stochasticΘ-method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochasticΘ-method is convergent of order1/2in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochasticΘ-method is mean-square asymptotically stable for every stepsize if1/2≤θ≤1and when0≤θ<1/2, the stochasticΘ-method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments.
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Yang, Hua, and Feng Jiang. "Stochasticθ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/589167.

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This paper is concerned with the convergence of stochasticθ-methods for stochastic pantograph equations with Poisson-driven jumps of random magnitude. The strong order of the convergence of the numerical method is given, and the convergence of the numerical method is obtained. Some earlier results are generalized and improved.
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Larson. "ON GENERALIZED STOCHASTIC CONVERGENCE." Real Analysis Exchange 20, no. 2 (1994): 450. http://dx.doi.org/10.2307/44152533.

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Robinson, P. M., and David Pollard. "Convergence of Stochastic Processes." Economica 52, no. 208 (November 1985): 529. http://dx.doi.org/10.2307/2553898.

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SABANIS, SOTIRIOS. "STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 05, no. 05 (August 2002): 515–30. http://dx.doi.org/10.1142/s021902490200150x.

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Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility. Although the option pricing formula has a power series representation, the question of convergence has been left unanswered. This paper presents an iterative method for calculating all the higher order moments of volatility necessary for the process of proving convergence theoretically. Moreover, simulation results are given that show the practical convergence of the series. These results have been obtained by using a displaced geometric Brownian motion as a volatility process.
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Szyszkowski, Ireneusz, and Ireneusz Szyszkowski. "Weak convergence of stochastic integrals." Teoriya Veroyatnostei i ee Primeneniya 41, no. 4 (1996): 942–46. http://dx.doi.org/10.4213/tvp3286.

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Ball, Frank, and Philip O'Neill. "Strong Convergence of Stochastic Epidemics." Advances in Applied Probability 26, no. 3 (September 1994): 629–55. http://dx.doi.org/10.2307/1427812.

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This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixing population in which new infections occur at rate f(x, y) and removals occur at rate g(x, y), where x and y are the numbers of susceptible and infective individuals, respectively, and f and g are arbitrary but specified positive real-valued functions. Sequences of such epidemics, indexed by the initial number of susceptibles n, are considered and conditions are derived under which the epidemic processes converge almost surely to a birth and death process as n tends to infinity. Thus a threshold theorem for such an epidemic model is obtained. The results are extended to models which incorporate immigration and emigration of susceptibles. The theory is illustrated by several examples of models taken from the epidemic literature. Generalizations to multipopulation epidemics are discussed briefly.
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Mello, Marcelo. "Stochastic Convergence Across Brazilian States." Brazilian Review of Econometrics 30, no. 1 (July 8, 2011): 23. http://dx.doi.org/10.12660/bre.v30n12010.2830.

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Dissertations / Theses on the topic "Stochastic convergence"

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Xiong, Xiaoping. "Stochastic optimization algorithms and convergence /." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2360.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.
Thesis research directed by: Business and Management. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Suzuki, Kohei. "Convergence of stochastic processes on varying metric spaces." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215281.

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Greensmith, Evan, and evan greensmith@gmail com. "Policy Gradient Methods: Variance Reduction and Stochastic Convergence." The Australian National University. Research School of Information Sciences and Engineering, 2005. http://thesis.anu.edu.au./public/adt-ANU20060106.193712.

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In a reinforcement learning task an agent must learn a policy for performing actions so as to perform well in a given environment. Policy gradient methods consider a parameterized class of policies, and using a policy from the class, and a trajectory through the environment taken by the agent using this policy, estimate the performance of the policy with respect to the parameters. Policy gradient methods avoid some of the problems of value function methods, such as policy degradation, where inaccuracy in the value function leads to the choice of a poor policy. However, the estimates produced by policy gradient methods can have high variance.¶ In Part I of this thesis we study the estimation variance of policy gradient algorithms, in particular, when augmenting the estimate with a baseline, a common method for reducing estimation variance, and when using actor-critic methods. A baseline adjusts the reward signal supplied by the environment, and can be used to reduce the variance of a policy gradient estimate without adding any bias. We find the baseline that minimizes the variance. We also consider the class of constant baselines, and find the constant baseline that minimizes the variance. We compare this to the common technique of adjusting the rewards by an estimate of the performance measure. Actor-critic methods usually attempt to learn a value function accurate enough to be used in a gradient estimate without adding much bias. In this thesis we propose that in learning the value function we should also consider the variance. We show how considering the variance of the gradient estimate when learning a value function can be beneficial, and we introduce a new optimization criterion for selecting a value function.¶ In Part II of this thesis we consider online versions of policy gradient algorithms, where we update our policy for selecting actions at each step in time, and study the convergence of the these online algorithms. For such online gradient-based algorithms, convergence results aim to show that the gradient of the performance measure approaches zero. Such a result has been shown for an algorithm which is based on observing trajectories between visits to a special state of the environment. However, the algorithm is not suitable in a partially observable setting, where we are unable to access the full state of the environment, and its variance depends on the time between visits to the special state, which may be large even when only few samples are needed to estimate the gradient. To date, convergence results for algorithms that do not rely on a special state are weaker. We show that, for a certain algorithm that does not rely on a special state, the gradient of the performance measure approaches zero. We show that this continues to hold when using certain baseline algorithms suggested by the results of Part I.
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Greensmith, Evan. "Policy gradient methods : variance reduction and stochastic convergence /." View thesis entry in Australian Digital Theses Program, 2005. http://thesis.anu.edu.au/public/adt-ANU20060106.193712/index.html.

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Sapozhnikov, Artyom Vasilyevich. "Existence of moments and convergence rates in stochastic networks." Thesis, Heriot-Watt University, 2005. http://hdl.handle.net/10399/256.

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Schiopu-Kratina, I. (Ioana). "General tightness conditions and weak convergence of point processes." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=71994.

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In this dissertation, we consider two aspects of the theory of weak convergence of cadlag processes.
We first give a necessary and sufficient condition for the tightness of a sequence of cadlag processes (chapters 2,3) which generalizes Rebolledo's condition (see 13 ). It is a stochastic condition in the sense that stopping times rather than deterministic times are used in the statement.
We then discuss the predictability of the limit of a sequence of predictable processes (chapters 4-6). For a convergent sequence of point processes we show that, if the sequence of compensators converges, then the limit of compensators is the compensator of the limit of point processes (chapters 4,5).
Finally, we prove in Chapter 6 that extended weak convergence of a sequence of increasing predictable processes ensures the predictability of the limit.
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Schmitz, Abe Klaus E. "Pricing exotic options using improved strong convergence." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:5a9fb837-238f-46a7-976a-fe3bae0e7b09.

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Today, better numerical approximations are required for multi-dimensional SDEs to improve on the poor performance of the standard Monte Carlo integration. With this aim in mind, the material in the thesis is divided into two main categories, stochastic calculus and mathematical finance. In the former, we introduce a new scheme or discrete time approximation based on an idea of Paul Malliavin where, for some conditions, a better strong convergence order is obtained than the standard Milstein scheme without the expensive simulation of the Lévy Area. We demonstrate when the conditions of the 2−Dimensional problem permit this and give an exact solution for the orthogonal transformation (θ Scheme or Orthogonal Milstein Scheme). Our applications are focused on continuous time diffusion models for the volatility and variance with their discrete time approximations (ARV). Two theorems that measure with confidence the order of strong and weak convergence of schemes without an exact solution or expectation of the system are formally proved and tested with numerical examples. In addition, some methods for simulating the double integrals or Lévy Area in the Milstein approximation are introduced. For mathematical finance, we review evidence of non-constant volatility and consider the implications for option pricing using stochastic volatility models. A general stochastic volatility model that represents most of the stochastic volatility models that are outlined in the literature is proposed. This was necessary in order to both study and understand the option price properties. The analytic closed-form solution for a European/Digital option for both the Square Root Model and the 3/2 Model are given. We present the Multilevel Monte Carlo path simulation method which is a powerful tool for pricing exotic options. An improved/updated version of the ML-MC algorithm using multi-schemes and a non-zero starting level is introduced. To link the contents of the thesis, we present a wide variety of pricing exotic option examples where considerable computational savings are demonstrated using the new θ Scheme and the improved Multischeme Multilevel Monte Carlo method (MSL-MC). The computational cost to achieve an accuracy of O(e) is reduced from O(e−3) to O(e−2) for some applications.
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Moon, Kyoung-Sook. "Convergence rates of adaptive algorithms for deterministic and stochastic differential equations." Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1382.

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von, Schwerin Erik. "Convergence rates of adaptive algorithms for stochastic and partial differential equations." Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302.

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Schwerin, Erik von. "Convergence rates of adaptive algorithms for stochastic and partial differential equations /." Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302.

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Books on the topic "Stochastic convergence"

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Chatterjee, Partha. Convergence in a stochastic dynamic Heckscher-Ohlin model. Ottawa: Bank of Canada, 2006.

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Prigent, Jean-Luc. Weak Convergence of Financial Markets. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.

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A. W. van der Vaart. Weak convergence and empirical processes. New York: Springer, 1996.

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Weak convergence methods and singularly perturbed stochastic control and filtering problems. Boston: Birkhäuser, 1990.

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Bai, Jushan. Stochastic equicontinuity and weak convergence of unbounded sequential empirical processes. Cambridge, Mass: Dept. of Economics, Massachusetts Institute of Technology, 1994.

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Prigent, Jean-Luc. Weak convergence of financial markets: Jean-Luc Prigent. Berlin: Springer, 2003.

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Weak convergence of financial markets: Jean-Luc Prigent. Berlin: Springer, 2003.

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Lee, Kevin. Growth and convergence in a multi-country empirical stochastic Solow model. Cairo: Economic Research Forum for the Arab Countries, Iran & Turkey, 1996.

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Down, Douglas G. Generalized minimum variance adaptive control and parameter convergence for stochastic systems. Ottawa: National Library of Canada, 1990.

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Kushner, Harold J. Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-4482-0.

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Book chapters on the topic "Stochastic convergence"

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Whittle, Peter. "Stochastic Convergence." In Springer Texts in Statistics, 282–89. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0509-8_16.

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Whittle, Peter. "Stochastic Convergence." In Springer Texts in Statistics, 235–42. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2892-9_13.

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Rudolph, Günter. "Stochastic Convergence." In Handbook of Natural Computing, 847–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-540-92910-9_27.

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Sen, Pranab Kumar, and Julio M. Singer. "Stochastic Convergence." In Large Sample Methods in Statistics, 31–95. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-4491-7_2.

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Kushner, Harold J., and G. George Yin. "Rate of Convergence." In Stochastic Approximation Algorithms and Applications, 273–325. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4899-2696-8_10.

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Kushner, Harold J., and G. George Yin. "Weak Convergence: Introduction." In Stochastic Approximation Algorithms and Applications, 185–212. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4899-2696-8_7.

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Carmona, René, and François Delarue. "Convergence and Approximations." In Probability Theory and Stochastic Modelling, 447–539. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-56436-4_6.

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Benveniste, Albert, Michel Métivier, and Pierre Priouret. "Rate of Convergence." In Adaptive Algorithms and Stochastic Approximations, 103–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75894-2_4.

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Micheas, Athanasios Christou. "Convergence of Random Objects." In Theory of Stochastic Objects, 183–206. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315156705-5.

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Kushner, Harold J. "Martingales and Weak Convergence." In Stochastic Modelling and Applied Probability, 45–87. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0005-2_2.

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Conference papers on the topic "Stochastic convergence"

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Bobrowski, Adam. "From convergence of operator semigroups to gene expression, and back again." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-5.

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Chen, Hui, and Lei Guo. "Convergence of a Stochastic Adaptive MPC." In 2021 40th Chinese Control Conference (CCC). IEEE, 2021. http://dx.doi.org/10.23919/ccc52363.2021.9549733.

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Chazal, Frédéric, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, and Larry Wasserman. "Stochastic Convergence of Persistence Landscapes and Silhouettes." In Annual Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2582112.2582128.

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Jin, Ruinan, and Xingkang He. "Convergence of Momentum-Based Stochastic Gradient Descent." In 2020 IEEE 16th International Conference on Control & Automation (ICCA). IEEE, 2020. http://dx.doi.org/10.1109/icca51439.2020.9264458.

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Huck, Stephan M., and John Lygeros. "Stochastic localization of sources with convergence guarantees." In 2013 European Control Conference (ECC). IEEE, 2013. http://dx.doi.org/10.23919/ecc.2013.6669538.

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Alrefaei, Mahmoud H., and Sigrún Andradóttir. "Accelerating the convergence of the stochastic ruler method for discrete stochastic optimization." In the 29th conference. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/268437.268506.

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Li, Shu, and Tamer Basar. "Asymptotic agreement and convergence of asynchronous stochastic algorithms." In 1986 25th IEEE Conference on Decision and Control. IEEE, 1986. http://dx.doi.org/10.1109/cdc.1986.267215.

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Eismann, Michael T., and Russell C. Hardie. "Initialization and convergence of the stochastic mixing model." In Optical Science and Technology, SPIE's 48th Annual Meeting, edited by Sylvia S. Shen and Paul E. Lewis. SPIE, 2004. http://dx.doi.org/10.1117/12.499680.

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Bedi, Amrit Singh, Hrusikesha Pradhan, and Ketan Rajawat. "Decentralized Asynchronous Stochastic Gradient Descent: Convergence Rate Analysis." In 2018 International Conference on Signal Processing and Communications (SPCOM). IEEE, 2018. http://dx.doi.org/10.1109/spcom.2018.8724408.

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Wang, Jieling, and Gang Xie. "Convergence of Stochastic Gradient Decent Algorithm with Momentum." In 2022 IEEE 2nd International Conference on Electronic Technology, Communication and Information (ICETCI). IEEE, 2022. http://dx.doi.org/10.1109/icetci55101.2022.9832402.

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Reports on the topic "Stochastic convergence"

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Glaser, R. Stochastic Engine Convergence Diagnostics. Office of Scientific and Technical Information (OSTI), December 2001. http://dx.doi.org/10.2172/15004940.

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DELAURENTIS, JOHN M., and IRENE MOSHESH. On the Convergence of Stochastic Finite Elements. Office of Scientific and Technical Information (OSTI), October 2001. http://dx.doi.org/10.2172/791887.

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Jaakkola, Tommi, Michael I. Jordan, and Satinder P. Singh. On the Convergence of Stochastic Iterative Dynamic Programming Algorithms. Fort Belvoir, VA: Defense Technical Information Center, August 1993. http://dx.doi.org/10.21236/ada276517.

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Fu, Michael C., and Xing Jin. Convergence of Sample Path Optimal Policies for Stochastic Dynamic Programming. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada438510.

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Dupuis, Paul, and Harold J. Kushner. Stochastic Approximation and Large Deviations: General Results for W.p.l. Convergence,. Fort Belvoir, VA: Defense Technical Information Center, February 1987. http://dx.doi.org/10.21236/ada185818.

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Tran, Hoang, Catalin Trenchea, and Clayton Webster. A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data. Office of Scientific and Technical Information (OSTI), January 2014. http://dx.doi.org/10.2172/1649669.

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