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Journal articles on the topic 'Nonlinear Expectation'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Ma, Jin, Ting-Kam Leonard Wong, and Jianfeng Zhang. "Time-Consistent Conditional Expectation Under Probability Distortion." Mathematics of Operations Research 46, no. 3 (August 2021): 1149–80. http://dx.doi.org/10.1287/moor.2020.1101.

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We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not subadditive in general, so it is beyond the scope of Peng’s framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time inconsistency, that is, the usual “tower property” fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step toward a new understanding of nonlinear expectations under probability distortion and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.

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2

Belak, Christoph, Thomas Seiferling, and Frank Thomas Seifried. "Backward nonlinear expectation equations." Mathematics and Financial Economics 12, no. 1 (August 23, 2017): 111–34. http://dx.doi.org/10.1007/s11579-017-0199-7.

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3

Ekren, Ibrahim, Nizar Touzi, and Jianfeng Zhang. "Optimal stopping under nonlinear expectation." Stochastic Processes and their Applications 124, no. 10 (October 2014): 3277–311. http://dx.doi.org/10.1016/j.spa.2014.04.006.

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4

Hu, Ying. "On Jensen’s inequality for g-expectation and for nonlinear expectation." Archiv der Mathematik 85, no. 6 (December 2005): 572–80. http://dx.doi.org/10.1007/s00013-005-1440-9.

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5

Liu, Guomin. "Exit times for semimartingales under nonlinear expectation." Stochastic Processes and their Applications 130, no. 12 (December 2020): 7338–62. http://dx.doi.org/10.1016/j.spa.2020.07.017.

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6

Anatolyev, Stanislav. "Nonparametric estimation of nonlinear rational expectation models." Economics Letters 62, no. 1 (January 1999): 1–6. http://dx.doi.org/10.1016/s0165-1765(98)00188-8.

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7

Dyke, C. "Expectation and strategy in a nonlinear world." Systems Research 7, no. 2 (June 1990): 117–25. http://dx.doi.org/10.1002/sres.3850070205.

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8

Qiao, Tianzhu, Yu Zhang, and Huaping Liu. "Nonlinear Expectation Maximization Estimator for TDOA Localization." IEEE Wireless Communications Letters 3, no. 6 (December 2014): 637–40. http://dx.doi.org/10.1109/lwc.2014.2364023.

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9

Rosipal, Roman, and Mark Girolami. "An Expectation-Maximization Approach to Nonlinear Component Analysis." Neural Computation 13, no. 3 (March 1, 2001): 505–10. http://dx.doi.org/10.1162/089976601300014439.

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The proposal of considering nonlinear principal component analysis as a kernel eigenvalue problem has provided an extremely powerful method of extracting nonlinear features for a number of classification and regression applications. Whereas the utilization of Mercer kernels makes the problem of computing principal components in, possibly, infinite-dimensional feature spaces tractable, there are still the attendant numerical problems of diagonalizing large matrices. In this contribution, we propose an expectation-maximization approach for performing kernel principal component analysis and show this to be a computationally efficient method, especially when the number of data points is large.

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10

ShiGe, PENG. "Theory, methods and meaning of nonlinear expectation theory." SCIENTIA SINICA Mathematica 47, no. 10 (July 19, 2017): 1223–54. http://dx.doi.org/10.1360/n012016-00209.

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11

Chen, Hung-Ju, and Ming-Chia Li. "Productive public expenditures, expectation formations and nonlinear dynamics." Mathematical Social Sciences 56, no. 1 (July 2008): 109–26. http://dx.doi.org/10.1016/j.mathsocsci.2007.11.002.

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12

Yang, B., and H. Xiao. "Law of large numbers under the nonlinear expectation." Proceedings of the American Mathematical Society 139, no. 10 (October 1, 2011): 3753. http://dx.doi.org/10.1090/s0002-9939-2011-10814-1.

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13

Song, Yunquan, and Lu Lin. "Sublinear Expectation Nonlinear Regression for the Financial Risk Measurement and Management." Discrete Dynamics in Nature and Society 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/398750.

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Financial risk is objective in modern financial activity. Management and measurement of the financial risks have become key abilities for financial institutions in competition and also make the major content in finance engineering and modern financial theories. It is important and necessary to model and forecast financial risk. We know that nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, specially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. In this paper, a sublinear expectation nonlinear regression is defined, and its identifiability is obtained. Several parameter estimations and model predictions are suggested, and the asymptotic normality of the estimation and the mini-max property of the prediction are obtained. Finally, simulation study and real data analysis are carried out to illustrate the new model and methods. In this paper, the notions and methodological developments are nonclassical and original, and the proposed modeling and inference methods establish the foundations for nonlinear expectation statistics.

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14

Chauvet, Marcelle, and Simon Potter. "NONLINEAR RISK." Macroeconomic Dynamics 5, no. 4 (September 2001): 621–46. http://dx.doi.org/10.1017/s1365100501023082.

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This paper analyzes the joint time-series properties of the level and volatility of expected excess stock returns. An unobservable dynamic factor is constructed as a nonlinear proxy for the market risk premia with its first moment and conditional volatility driven by a latent Markov variable. The model allows for the possibility that the risk–return relationship may not be constant across the Markov states or over time. We find an overall negative contemporaneous relationship between the conditional expectation and variance of the monthly value-weighted excess return. However, the sign of the correlation is not stable, but instead varies according to the stage of the business cycle. In particular, around the beginning of recessions, volatility rises substantially, reflecting great uncertainty associated with these periods, while expected return falls, anticipating a decline in earnings. Thus, around economic peaks there is a negative relationship between conditional expectation and variance. However, toward the end of a recession expected return is at its highest value as an anticipation of the economic recovery, and volatility is still very high in anticipation of the end of the contraction. That is, the risk–return relation is positive around business-cycle troughs. This time-varying behavior also holds for noncontemporaneous correlations of these two conditional moments.

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15

Nutz, Marcel, and Jianfeng Zhang. "Optimal stopping under adverse nonlinear expectation and related games." Annals of Applied Probability 25, no. 5 (October 2015): 2503–34. http://dx.doi.org/10.1214/14-aap1054.

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16

Vondřejc, Jaroslav, and Hermann G. Matthies. "Accurate Computation of Conditional Expectation for Highly Nonlinear Problems." SIAM/ASA Journal on Uncertainty Quantification 7, no. 4 (January 2019): 1349–68. http://dx.doi.org/10.1137/18m1196674.

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17

Zhang, Miao, and Zeng-jing Chen. "A law of large numbers under the nonlinear expectation." Acta Mathematicae Applicatae Sinica, English Series 31, no. 4 (October 2015): 953–62. http://dx.doi.org/10.1007/s10255-015-0514-0.

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18

Hartung, T., and K. Jansen. "Zeta-regularized vacuum expectation values." Journal of Mathematical Physics 60, no. 9 (September 2019): 093504. http://dx.doi.org/10.1063/1.5085866.

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19

Nigh, Gordon. "Calculating empirical best linear unbiased predictors (EBLUPs) for nonlinear mixed effects models in Excel/Solver." Forestry Chronicle 88, no. 03 (June 2012): 340–44. http://dx.doi.org/10.5558/tfc2012-061.

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Nonlinear mixed-effects models have become common in the forestry literature. Calibration of these models for a new subject (one not used in the fitting of the model) involves estimating the values of the of random-effects parameters. Estimators can be obtained by taking a Taylor-series expansion of the nonlinear model around the expected value or the conditional expectation of the random-effects parameters. The conditional expectation method requires an iterative technique to find the estimates, which can be a complicated programming exercise. This note describes a relatively easy way to do the calculations necessary for both the zero expansion and conditional expectation methods in Excel and demonstrates the procedure on a small example.

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20

Gao, Lei, and Dong Han. "Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation." Mathematics 7, no. 1 (January 4, 2019): 45. http://dx.doi.org/10.3390/math7010045.

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In this paper, we consider a special nonlinear expectation problem on the special parameter space and give a necessary and sufficient condition for the existence of the solution. Meanwhile, we generalize the necessary and sufficient condition to the two-dimensional moment problem. Moreover, we use the maximum entropy method to carry out a kind of concrete solution and analyze the convergence for the maximum entropy solution. Numerical experiments are presented to compute the maximum entropy density functions.

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21

Zhang, Na, and Guang-yan Jia. "Jensen’s Inequality Under Nonlinear Expectation Generated by BSDE with Jumps." Acta Mathematicae Applicatae Sinica, English Series 35, no. 4 (September 2019): 873–84. http://dx.doi.org/10.1007/s10255-019-0862-1.

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22

Fan, Sheng-Jun. "Jensen's inequality for filtration consistent nonlinear expectation without domination condition." Journal of Mathematical Analysis and Applications 345, no. 2 (September 2008): 678–88. http://dx.doi.org/10.1016/j.jmaa.2008.04.037.

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23

MADAN, DILIP B., MARTIJN PISTORIUS, and WIM SCHOUTENS. "CONIC TRADING IN A MARKOVIAN STEADY STATE." International Journal of Theoretical and Applied Finance 20, no. 02 (March 2017): 1750010. http://dx.doi.org/10.1142/s0219024917500108.

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Trading strategies are valued using nonlinear conditional expectations based on concave probability distortions. They are also referred to as expectation with respect to a nonadditive probability. The nonadditive probability attains conservatism by exaggerating upwards the probabilities of tail loss events and simultaneously deflating the probabilities of tail gain events. Fixed points for value and policy iterations are obtained when probabilities are distorted and they fail to exist for classical linear or additive expectations. Illustrations are provided for Markovian systems in one, two and five dimensions. Trading positions are seen to balance prediction rewards against the demands for hedging value functions.

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24

Cerreia-Vioglio, S., F. Maccheroni, M. Marinacci, and L. Montrucchio. "Commutativity, comonotonicity, and Choquet integration of self-adjoint operators." Reviews in Mathematical Physics 30, no. 10 (October 12, 2018): 1850016. http://dx.doi.org/10.1142/s0129055x18500162.

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In this work, we propose a definition of comonotonicity for elements of [Formula: see text], i.e. bounded self-adjoint operators defined over a complex Hilbert space [Formula: see text]. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of [Formula: see text] that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over [Formula: see text] which are comonotonic additive, [Formula: see text]-monotone, and normalized.

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25

Killingbeck, J. "Direct expectation value calculations." Journal of Physics A: Mathematical and General 18, no. 2 (February 1, 1985): 245–52. http://dx.doi.org/10.1088/0305-4470/18/2/014.

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26

Zinoviev, Yu M. "Vacuum expectation values of quantum fields." Theoretical and Mathematical Physics 157, no. 1 (October 2008): 1399–419. http://dx.doi.org/10.1007/s11232-008-0116-6.

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27

Chithiika Ruby, V., P. Muruganandam, and M. Senthilvelan. "Nonlinear time evolution of coherent states with observation of super revivals in a generalized isotonic oscillator." International Journal of Geometric Methods in Modern Physics 11, no. 04 (April 2014): 1450027. http://dx.doi.org/10.1142/s0219887814500273.

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In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

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28

Zhang, J., S. S. Dlay, and W. L. Woo. "Expectation–maximisation approach to blind source separation of nonlinear convolutive mixture." IET Signal Processing 1, no. 2 (June 1, 2007): 51–65. http://dx.doi.org/10.1049/iet-spr:20065009.

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29

Ypma, Alexander, and Tom Heskes. "Novel approximations for inference in nonlinear dynamical systems using expectation propagation." Neurocomputing 69, no. 1-3 (December 2005): 85–99. http://dx.doi.org/10.1016/j.neucom.2005.02.020.

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30

GARBACZEWSKI, PIOTR. "CANONICAL ACTION-ANGLE FORMALISM FOR QUANTIZED NONLINEAR FIELDS." International Journal of Modern Physics A 02, no. 01 (February 1987): 223–48. http://dx.doi.org/10.1142/s0217751x87000090.

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The canonical quantizations of field and action-angle coordinates which (locally) parametrize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrödinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects.

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31

Dias, N. C., A. Miković, and J. N. Prata. "Coherent states expectation values as semiclassical trajectories." Journal of Mathematical Physics 47, no. 8 (August 2006): 082101. http://dx.doi.org/10.1063/1.2227259.

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32

Delbourgo, R., and D. Elliott. "Inverse momentum expectation values for hydrogenic systems." Journal of Mathematical Physics 50, no. 6 (June 2009): 062107. http://dx.doi.org/10.1063/1.3141534.

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33

Guo, Yanbing, Lingjuan Miao, and Yusen Lin. "A Novel EM Implementation for Initial Alignment of SINS Based on Particle Filter and Particle Swarm Optimization." Mathematical Problems in Engineering 2019 (February 20, 2019): 1–12. http://dx.doi.org/10.1155/2019/6793175.

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For nonlinear systems in which the measurement noise parameters vary over time, adaptive nonlinear filters can be applied to precisely estimate the states of systems. The expectation maximization (EM) algorithm, which alternately takes an expectation- (E-) step and a maximization- (M-) step, has been proposed to construct a theoretical framework for the adaptive nonlinear filters. Previous adaptive nonlinear filters based on the EM employ analytical algorithms to develop the two steps, but they cannot achieve high filtering accuracy because the strong nonlinearity of systems may invalidate the Gaussian assumption of the state distribution. In this paper, we propose an EM-based adaptive nonlinear filter APF to solve this problem. In the E-step, an improved particle filter PF_new is proposed based on the Gaussian sum approximation (GSA) and the Monte Carlo Markov chain (MCMC) to achieve the state estimation. In the M-step, the particle swarm optimization (PSO) is applied to estimate the measurement noise parameters. The performances of the proposed algorithm are illustrated in the simulations with Lorenz 63 model and in a semiphysical experiment of the initial alignment of the strapdown inertial navigation system (SINS) in large misalignment angles.

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34

Fan, Yulian, and Huadong Zhang. "The Pricing of Asian Options in Uncertain Volatility Model." Mathematical Problems in Engineering 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/786391.

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This paper studies the pricing of Asian options when the volatility of the underlying asset is uncertain. We use the nonlinear Feynman-Kac formula in the G-expectation theory to get the two-dimensional nonlinear PDEs. For the arithmetic average fixed strike Asian options, the nonlinear PDEs can be transferred to linear PDEs. For the arithmetic average floating strike Asian options, we use a dimension reduction technique to transfer the two-dimensional nonlinear PDEs to one-dimensional nonlinear PDEs. Then we introduce the applicable numerical computation methods for these two classes of PDEs and analyze the performance of the numerical algorithms.

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35

Yang, Yuqing, and Shongming Huang. "Comparison of different methods for fitting nonlinear mixed forest models and for making predictions." Canadian Journal of Forest Research 41, no. 8 (August 2011): 1671–86. http://dx.doi.org/10.1139/x11-071.

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Nonlinear mixed models have become popular in forestry applications, and various methods have been proposed for fitting such models. However, it is difficult or even confusing to choose which method to use, and there is not much relevant information available, especially in the forestry context. The main objective of this study was to compare three commonly used methods for fitting nonlinear mixed models: the first-order, the first-order conditional expectation, and the adaptive Gaussian quadrature methods. Both the maximum likelihood and restricted maximum likelihood parameter estimation techniques were evaluated. Three types of data common in forestry were used for model fitting and model application. It was found that the first-order conditional expectation method provided more accurate and precise predictions for two models developed from data with more observations per subject. For one model developed on data with fewer observations per subject, the first-order method provided better model predictions. All three models fitted by the first-order method produced some biologically unrealistic predictions, and the problem was more obvious on the data with fewer observations per subject. For all three models fitted by the first-order and first-order conditional expectation methods, the maximum likelihood and restricted maximum likelihood fits and the resulting model predictions were very close.

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36

Zheng, Zhonghao, Xiuchun Bi, and Shuguang Zhang. "Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/564524.

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We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in Zhang (2011). Then we obtain a generalized dynamic programming principle, and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.

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37

SCHULZE, CHRISTIAN. "SORNETTE–IDE MODEL FOR MARKETS: TRADER EXPECTATIONS AS IMAGINARY PART." International Journal of Modern Physics C 13, no. 04 (May 2002): 551–53. http://dx.doi.org/10.1142/s0129183102003310.

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A nonlinear differential equation of Sornette–Ide type with noise, for a complex variable, yields endogenous crashes, preceded by roughly log-periodic oscillations in the real part, and a strong increase in the imaginary part. The latter is interpreted as the trader expectation.

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38

MISHCHENKO, YURIY, and CHUENG-RYONG JI. "A NOVEL VARIATIONAL APPROACH FOR QUANTUM FIELD THEORY: EXAMPLE OF STUDY OF THE GROUND STATE AND PHASE TRANSITION IN NONLINEAR SIGMA MODEL." International Journal of Modern Physics A 20, no. 15 (June 20, 2005): 3488–94. http://dx.doi.org/10.1142/s0217751x05026819.

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We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from Fock space. The quantum algebra imposes constraints on such expectation values so that the variational problem is formulated here as an optimization under constraints. As an example of application of such approach we consider the study of ground state and critical properties in a variant of nonlinear sigma model.

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39

Chen, Xiaohong, Lars Peter Hansen, and Peter G. Hansen. "Robust identification of investor beliefs." Proceedings of the National Academy of Sciences 117, no. 52 (December 14, 2020): 33130–40. http://dx.doi.org/10.1073/pnas.2019910117.

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This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macrofinance using asset market data to infer belief restrictions for macroeconomic growth rates.

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40

Gheorghe, Andreea, Oana Fodor, and Anișoara Pavelea. "Ups and downs on the roller coaster of task conflict: the role of group cognitive complexity, collective emotional intelligence and team creativity." Psihologia Resurselor Umane 18, no. 1 (May 19, 2020): 23–37. http://dx.doi.org/10.24837/pru.v18i1.459.

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This study explores the association between task conflict and team creativity and the role of group cognitive complexity (GCC) as a potential explanatory mechanism in a sample of 159 students organized in 49 groups. Moreover, we analyzed the moderating effect of collective emotional intelligence (CEI)in the relationship between task conflict and GCC.As hypothesized, we found that task conflict has a nonlinear relationship with GCC, but contrary to our expectations, it follows a U-shaped association, not an inversed U-shape. In addition,the moderating role of CEI was significant only at low levels. Contrary to our expectation, the mediating role of GCC did not receive empirical support. Theoretical and practical contributions are discussed.

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41

Miyahara, Hideyuki, Koji Tsumura, and Yuki Sughiyama. "Deterministic quantum annealing expectation-maximization algorithm." Journal of Statistical Mechanics: Theory and Experiment 2017, no. 11 (November 17, 2017): 113404. http://dx.doi.org/10.1088/1742-5468/aa967e.

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42

Heskes, Tom, Manfred Opper, Wim Wiegerinck, Ole Winther, and Onno Zoeter. "Approximate inference techniques with expectation constraints." Journal of Statistical Mechanics: Theory and Experiment 2005, no. 11 (November 30, 2005): P11015. http://dx.doi.org/10.1088/1742-5468/2005/11/p11015.

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43

Barletti, L., and G. Busoni. "Deterministic effective equations for the propagation of expectation in noisy nonlinear optical fibers." Mathematical Methods in the Applied Sciences 33, no. 10 (May 7, 2010): 1221–27. http://dx.doi.org/10.1002/mma.1323.

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44

Mili, Medhi, Jean-Michel Sahut, and Fredéric Teulon. "New evidence of the expectation hypothesis of interest rates: a flexible nonlinear approach." Applied Financial Economics 22, no. 2 (October 3, 2011): 165–76. http://dx.doi.org/10.1080/09603107.2011.607127.

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45

Gehre, Matthias, and Bangti Jin. "Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography." Journal of Computational Physics 259 (February 2014): 513–35. http://dx.doi.org/10.1016/j.jcp.2013.12.010.

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46

Koch, Karl-Rudolf. "Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm." Journal of Geodesy 88, no. 3 (December 15, 2013): 263–71. http://dx.doi.org/10.1007/s00190-013-0681-9.

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47

Ge, Ming, and Eric C. Kerrigan. "Noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation." Automatica 77 (March 2017): 336–43. http://dx.doi.org/10.1016/j.automatica.2016.11.011.

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48

Salmhofer, Manfred. "Clustering of Fermionic Truncated Expectation Values Via Functional Integration." Journal of Statistical Physics 134, no. 5-6 (March 2009): 941–52. http://dx.doi.org/10.1007/s10955-009-9698-0.

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49

Čižmešija, Mirjana, Zrinka Lukač, and Tomislav Novoselec. "Nonlinear optimisation approach to proposing novel Croatian Industrial Confidence Indicator." Croatian Review of Economic, Business and Social Statistics 5, no. 2 (December 1, 2019): 17–26. http://dx.doi.org/10.2478/crebss-2019-0008.

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AbstractCroatian Industrial Confidence Indicator (ICI) is one of the measures of mangers’ sentiment about the economic situation in the Croatian manufacturing industry. Since 2005, the ICI has been calculated in accordance with the harmonised European Commission methodology as a simple average of three variables: order books, stocks of finished products and production expectation. It was empirically confirmed that the ICI could predict the direction of change in industrial production more than one month ahead. With the aim of raising the ICI forecasting power, this paper proposes a novel ICI with a different weighting scheme. The empirical analysis is based on monthly data for three standard ICI subcomponents and industrial production expressed as year-on-year growth rates. The data set covers the period from May 2008 to February 2019. Data sources were the European Commission and Eurostat. The newly defined ICI was constructed by using the nonlinear optimisation approach. The weights were determined by minimizing the root mean square error (RMSE) in a simple regression model and by maximizing the correlation coefficient between the ICI and industrial production for various time lags. The results reveal that the newly defined ICI performs better in adapting and following the industrial production growth rate as well as that the dominant component in the ICI is the production expectation.

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50

Egorov, A. D. "On composite formulas for mathematical expectation of functionals of solution of the Ito equation in Hilbert space." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 2 (June 28, 2019): 158–68. http://dx.doi.org/10.29235/1561-2430-2019-55-2-158-168.

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Abstract:

This article is devoted to constructing composite approximate formulas for calculation of mathematical expectation of nonlinear functionals of solution of the linear Ito equation in Hilbert space with additive noise. As the leading process, the Wiener process taking values in Hilbert space is examined. The formulas are a sum of the approximations of the nonlinear functionals obtained by expanding the leading random process into a series of independent Gaussian random variables and correcting approximating functional quadrature formulas that ensure an approximate accuracy of compound formulas for third-order polynomials. As a test example, the application of the obtained formulas to the case of a one-dimensional wave equation with a leading Wiener process indexed by spatial and temporal variables is considered. This article continues the research begun in [1].The problem is motivated by the necessity to calculate the nonlinear functionals of solution of stochastic partial differential equations. Approximate evaluation of mathematical expectation of stochastic equations with a leading random process indexed only by the time variable is considered in [2–11]. Stochastic partial equations in various interpretations are considered [12–16]. The present article uses the approach given in [12].

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