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Journal articles on the topic 'Stochastic convergence'

To see the other types of publications on this topic, follow the link: Stochastic convergence.

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

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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2

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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3

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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4

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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5

Larson. "ON GENERALIZED STOCHASTIC CONVERGENCE." Real Analysis Exchange 20, no. 2 (1994): 450. http://dx.doi.org/10.2307/44152533.

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6

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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7

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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8

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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9

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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10

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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11

Shapiro, A., and Y. Wardi. "Convergence Analysis of Stochastic Algorithms." Mathematics of Operations Research 21, no. 3 (August 1996): 615–28. http://dx.doi.org/10.1287/moor.21.3.615.

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12

Hansen, Bruce E. "Convergence to a Stochastic Integral." Econometric Theory 6, no. 4 (December 1990): 485. http://dx.doi.org/10.1017/s0266466600005508.

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13

Dolado, Juan J. "Convergence to a Stochastic Integral." Econometric Theory 8, no. 01 (March 1992): 148–50. http://dx.doi.org/10.1017/s0266466600010872.

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14

Mello, Marcelo. "STOCHASTIC CONVERGENCE ACROSS U.S. STATES." Macroeconomic Dynamics 15, no. 2 (February 26, 2010): 160–83. http://dx.doi.org/10.1017/s1365100509991106.

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Unit root tests suggest that shocks to relative income across U.S. states are permanent, which contradicts the stochastic convergence hypothesis. We suggest that this finding is due to the well-known low-power problem of unit root tests in the presence of high persistence (i.e., low speed of convergence) and small samples. First, interval estimates of the largest autoregressive root for the relative income in the 48 U.S. contiguous states are quite wide, including many alternatives that are persistent but stable. Second, interval estimates of the half-life of relative income shocks that are robust to high persistence and small samples suggest that in most cases shocks die out within zero to ten years. Third, estimation of a fractionally integrated model for the relative income process suggests strong evidence of mean reversion in the data. These findings provide ample support for the stochastic convergence hypothesis.

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15

Ball, Frank, and Philip O'Neill. "Strong Convergence of Stochastic Epidemics." Advances in Applied Probability 26, no. 03 (September 1994): 629–55. http://dx.doi.org/10.1017/s000186780002646x.

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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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16

Lin, Zhengyan, and Hanchao Wang. "On Convergence to Stochastic Integrals." Journal of Theoretical Probability 29, no. 3 (January 31, 2015): 717–36. http://dx.doi.org/10.1007/s10959-015-0598-8.

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17

Beran, R. J., L. Le Cam, and P. W. Millar. "Convergence of stochastic empirical measures." Journal of Multivariate Analysis 23, no. 1 (October 1987): 159–68. http://dx.doi.org/10.1016/0047-259x(87)90183-7.

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18

Lluís Carrion-I-Silvestre, Josep, and Vicente German-Soto. "Stochastic Convergence amongst Mexican States." Regional Studies 41, no. 4 (June 2007): 531–41. http://dx.doi.org/10.1080/00343400601120221.

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19

Birge, John R., and Liqun Qi. "Subdifferential Convergence in Stochastic Programs." SIAM Journal on Optimization 5, no. 2 (May 1995): 436–53. http://dx.doi.org/10.1137/0805022.

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20

Sango, Mamadou, and Jean Louis Woukeng. "Stochastic Σ-convergence and applications." Dynamics of Partial Differential Equations 8, no. 4 (2011): 261–310. http://dx.doi.org/10.4310/dpde.2011.v8.n4.a1.

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21

Garnier, Josselin, George Papanicolaou, and Tzu-Wei Yang. "Consensus Convergence with Stochastic Effects." Vietnam Journal of Mathematics 45, no. 1-2 (March 18, 2016): 51–75. http://dx.doi.org/10.1007/s10013-016-0190-2.

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22

Ermoliev, Yuri M., and Vladimir I. Norkin. "Normalized convergence in stochastic optimization." Annals of Operations Research 30, no. 1 (December 1991): 187–98. http://dx.doi.org/10.1007/bf02204816.

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23

Ejima, Toshiaki. "Convergence of stochastic relaxation process." Electronics and Communications in Japan (Part I: Communications) 71, no. 9 (September 1988): 36–43. http://dx.doi.org/10.1002/ecja.4410710905.

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24

Kurniati, Azwardi, and Sukanto. "Economic Convergence in Sumatra Island: Stochastic Approach." MIR (Modernization. Innovation. Research) 13, no. 1 (March 30, 2022): 60–72. http://dx.doi.org/10.18184/2079-4665.2022.13.4.60-72.

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Purpose: convergence occurs when regions with poor economies tend to grow faster than regions with rich economies, so poorer regions tend to catch up with rich regions in terms of GRDP or per capita products. The concept of convergence is dividedinto3 (three) namely sigma convergence, absolute convergence, and conditional convergence. This study focuses on analyzing the trend of convergence based on the approach to the concept of convergence with a concern for analysis, namely stochastic convergence.Methods: the analysis of convergence using a stochastic approach and a sigma and beta convergence approach for each province on the island ofSumatraduringthe2011–2020 periods. This research data uses secondary data with a combination of time-series data and cross-sectional data obtained from the Central Statistics Agency, the Ministry of Finance, and the Investment Coordinating Board. Calculation of beta convergence is based on the equation model developed by Barro and Sala-I-Martin (1990) and stochastic convergence based on the measurement model by Ludlow and Enders (2000).Results: the finding from this study shows that there is a stochastic convergence in all provinces on the island of Sumatra which is described based on the Sumatra. The economy has proven Beta convergence which explains the convergence with a relatively low rate of convergence, but the addition of determinant variables such as Domestic Investment and government spending has an impact on increasing the rate of convergence in the island of Sumatra.Conclusions and Relevance: the recommendation for further research emphasizes the spatial interaction between regions because the stochastic stocked test has not been able to see the interdependence between regions that causes convergence.

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25

Heida, Martin, Stefan Neukamm, and Mario Varga. "Stochastic two-scale convergence and Young measures." Networks and Heterogeneous Media 17, no. 2 (2022): 227. http://dx.doi.org/10.3934/nhm.2022004.

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<p style='text-indent:20px;'>In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover, we discuss two examples, which can be naturally analyzed via stochastic unfolding, but which cannot be treated via quenched stochastic two-scale convergence.</p>

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26

Tleubergenov, Marat, Gulmira Vassilina, and Darkhan Azhymbaev. "Stochastic Helmholtz problem and convergence in distribution." Filomat 36, no. 7 (2022): 2451–60. http://dx.doi.org/10.2298/fil2207451t.

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In the present paper, the solvability of the stochastic Helmholtz problem is investigated in the class of stochastic differential equations equivalent in distribution. Earlier, by additional variables method the Helmholtz problem was investigated in the class of stochastic differential equations equivalent almost surely (a.s.). The study of the stochastic Helmholtz problem in the class of equations equivalent in distribution allows us to significantly expand the region of its solvability. This is due to the possibility of using well-known methods of the theory of stochastic processes, such as the method of the phase space transformation, the method of absolutely continuous change of measure, and the method of random change of time. In that paper stochastic equations of the Lagrangian structure equivalent in distribution are constructed by the given second order Ito stochastic equations using the methods of phase space transformation, absolutely continuous measure transformation and randomtime substitution. The obtained results are illustrated by specific examples.

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27

Jaakkola, Tommi, Michael I. Jordan, and Satinder P. Singh. "On the Convergence of Stochastic Iterative Dynamic Programming Algorithms." Neural Computation 6, no. 6 (November 1994): 1185–201. http://dx.doi.org/10.1162/neco.1994.6.6.1185.

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Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(λ) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(λ) and Q-learning belong.

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28

Plachky, D. "A simple characterization of almost uniform convergence by stochastic convergence." Manuscripta Mathematica 69, no. 1 (December 1990): 27–30. http://dx.doi.org/10.1007/bf02567910.

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29

Próchniak, Mariusz, and Bartosz Witkowski. "On the use of panel stationarity tests in convergence analysis: empirical evidence for the EU countries." Equilibrium 11, no. 1 (March 31, 2016): 77. http://dx.doi.org/10.12775/equil.2016.004.

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The study examines the concept of stochastic convergence in the EU28 countries over the 1994–2013 period. The convergence of individual countries’ GDP per capita towards the EU28 average per capita income level and the pair-wise convergence between the GDP of individual countries are both analyzed. Additionally, we introduce our own concept of conditional stochastic convergence which is based on adjusted GDP per capita series in order to account for the impact of other growth factors on GDP. The analysis is based on time series techniques. To assess stationarity, ADF tests are used. The study shows that the process of stochastic convergence in the EU countries is not as widespread as the cross-sectional studies on b or s convergence indicate. Even if we extend the analysis to examine conditional stochastic convergence, the number of converging economies or pairs of countries rises, but not as much as it could be expected from the cross-sectional studies.

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30

Hashemi, Fariba. "Stochastic Convergence in Regional Economic Activity." Journal of Mathematical Finance 01, no. 03 (2011): 125–31. http://dx.doi.org/10.4236/jmf.2011.13016.

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31

Chen, Han-Fu, and Ji-Feng Zhang. "Convergence rates in stochastic adaptive tracking." International Journal of Control 49, no. 6 (June 1989): 1915–35. http://dx.doi.org/10.1080/00207178908559752.

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32

NASUTO, S., and M. BISHOP. "CONVERGENCE ANALYSIS OF STOCHASTIC DIFFUSION SEARCH." Parallel Algorithms and Applications 14, no. 2 (July 1999): 89–107. http://dx.doi.org/10.1080/10637199808947380.

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33

Hoshino, Kenta, Yûki Nishimura, and Yuh Yamashita. "Convergence rates of stochastic homogeneous systems." Systems & Control Letters 124 (February 2019): 33–39. http://dx.doi.org/10.1016/j.sysconle.2018.11.013.

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34

Chen, Han-Fu, and Katsuji Uosaki. "Convergence analysis of dynamic stochastic approximation." Systems & Control Letters 35, no. 5 (December 1998): 309–15. http://dx.doi.org/10.1016/s0167-6911(98)00077-2.

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35

Drmota, Michael, and Jean-François Marckert. "Reinforced weak convergence of stochastic processes." Statistics & Probability Letters 71, no. 3 (March 2005): 283–94. http://dx.doi.org/10.1016/j.spl.2004.11.005.

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36

Lythe, Grant, and Salman Habib. "Stochastic PDEs: convergence to the continuum?" Computer Physics Communications 142, no. 1-3 (December 2001): 29–35. http://dx.doi.org/10.1016/s0010-4655(01)00308-3.

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37

Arcones, Miguel A. "Weak convergence of convex stochastic processes." Statistics & Probability Letters 37, no. 2 (February 1998): 171–82. http://dx.doi.org/10.1016/s0167-7152(97)00115-6.

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38

Rosasco, Lorenzo, Silvia Villa, and Bằng Công Vũ. "Convergence of Stochastic Proximal Gradient Algorithm." Applied Mathematics & Optimization 82, no. 3 (October 15, 2019): 891–917. http://dx.doi.org/10.1007/s00245-019-09617-7.

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39

Rhee, Wansoo T. "Convergence of optimal stochastic bin packing." Operations Research Letters 4, no. 3 (October 1985): 121–23. http://dx.doi.org/10.1016/0167-6377(85)90015-x.

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40

Bespalov, Alex, Dirk Praetorius, Leonardo Rocchi, and Michele Ruggeri. "Convergence of Adaptive Stochastic Galerkin FEM." SIAM Journal on Numerical Analysis 57, no. 5 (January 2019): 2359–82. http://dx.doi.org/10.1137/18m1229560.

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41

Chen, Han-Fu, and Ji-Feng Zhang. "Convergence rates in stochastic adaptive tracking†." International Journal of Control 49, no. 6 (June 1, 1989): 1915–35. http://dx.doi.org/10.1080/00207178908961362.

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42

Morkvenas, R. "Convergence of two-parameter stochastic processes." Lithuanian Mathematical Journal 27, no. 4 (1988): 334–39. http://dx.doi.org/10.1007/bf00966263.

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43

Funai, Naoki. "Convergence results on stochastic adaptive learning." Economic Theory 68, no. 4 (September 21, 2018): 907–34. http://dx.doi.org/10.1007/s00199-018-1150-8.

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44

Hiroshi, Kunita. "Convergence of stochastic flows connected with stochastic ordinary differential equations." Stochastics 17, no. 3 (May 1986): 215–51. http://dx.doi.org/10.1080/17442508608833391.

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45

Li, Fengzhong, and Yungang Liu. "General Stochastic Convergence Theorem and Stochastic Adaptive Output-Feedback Controller." IEEE Transactions on Automatic Control 62, no. 5 (May 2017): 2334–49. http://dx.doi.org/10.1109/tac.2016.2604498.

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46

Barone, Piero, and Arnolodo Frigessi. "Improving Stochastic Relaxation for Gussian Random Fields." Probability in the Engineering and Informational Sciences 4, no. 3 (July 1990): 369–89. http://dx.doi.org/10.1017/s0269964800001674.

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In this paper, we are concerned with the simulation of Gaussian random fields by means of iterative stochastic algorithms, which are compared in terms of rate of convergence. A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established. A suitable choice for the parameter improves the rate of convergence with respect to stochastic relaxation for special classes of covariance matrices. Some examples and numerical experiments are given.

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47

Kloeden, P. E., and A. Neuenkirch. "The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations." LMS Journal of Computation and Mathematics 10 (2007): 235–53. http://dx.doi.org/10.1112/s1461157000001388.

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AbstractThe authors of this paper study approximation methods for stochastic differential equations, and point out a simple relation between the order of convergence in the pth mean and the order of convergence in the pathwise sense: Convergence in the pth mean of order α for all p ≥ 1 implies pathwise convergence of order α – ε for arbitrary ε > 0. The authors then apply this result to several one-step and multi-step approximation schemes for stochastic differential equations and stochastic delay differential equations. In addition, they give some numerical examples.

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48

Li, Gang, Minghua Li, and Yaohua Hu. "Stochastic quasi-subgradient method for stochastic quasi-convex feasibility problems." Discrete & Continuous Dynamical Systems - S 15, no. 4 (2022): 713. http://dx.doi.org/10.3934/dcdss.2021127.

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<p style='text-indent:20px;'>The feasibility problem is at the core of the modeling of many problems in various disciplines of mathematics and physical sciences, and the quasi-convex function is widely applied in many fields such as economics, finance, and management science. In this paper, we consider the stochastic quasi-convex feasibility problem (SQFP), which is to find a common point of infinitely many sublevel sets of quasi-convex functions. Inspired by the idea of a stochastic index scheme, we propose a stochastic quasi-subgradient method to solve the SQFP, in which the quasi-subgradients of a random (and finite) index set of component quasi-convex functions at the current iterate are used to construct the descent direction at each iteration. Moreover, we introduce a notion of Hölder-type error bound property relative to the random control sequence for the SQFP, and use it to establish the global convergence theorem and convergence rate theory of the stochastic quasi-subgradient method. It is revealed in this paper that the stochastic quasi-subgradient method enjoys both advantages of low computational cost requirement and fast convergence feature.</p>

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49

Lu, Zhenyu, Tingya Yang, Yanhan Hu, and Junhao Hu. "Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/420648.

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The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.

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50

You, Pin, Yunpeng Sun, and Lei An. "Nominal and Real Stochastic Convergence of the BRICS Economies." Review of Economic and Business Studies 10, no. 2 (December 1, 2017): 9–28. http://dx.doi.org/10.1515/rebs-2017-0052.

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AbstractThis study sheds light on the real and nominal economic convergence and the time-varying convergence speed of Brazil, Russia, India, China, and South Africa (BRICS). This paper also employs panel data models and a Malmquist index to analyze the mechanism of real economic convergence. The study finds evidence of real convergence in monthly growth of output (industrial production) of the BRICS economies, where the speed of convergence increases in the post-crisis period. Economic convergence is also witnessed by physical capital per capita and total factor productivity (TFP). However, lack of monetary convergence is apparent in nominal interest rate spreads, monetary aggregate M2, and the price level. Although the BRICS economies are converging to a fully-fledged economic and trade union, such convergence is not echoed by their monetary aggregates and price levels. Finally, the evidence of technological progress is expected to promote labor productivity and to further accelerate economic convergence.

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