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Articles de revues sur le sujet « Continuous-time stochastic models »

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Auteur : Grafiati
Publié le 10 mars 2023

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1

SÖDERSTROM, TORSTEN. « Computing stochastic continuous-time models from ARMA models ». International Journal of Control 53, no 6 (juin 1991) : 1311–26. http://dx.doi.org/10.1080/00207179108953677.

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2

Comte, F., et E. Renault. « Noncausality in Continuous Time Models ». Econometric Theory 12, no 2 (juin 1996) : 215–56. http://dx.doi.org/10.1017/s0266466600006575.

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In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.
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3

Cvitanić, Jakša, Xuhu Wan et Jianfeng Zhang. « Optimal contracts in continuous-time models ». Journal of Applied Mathematics and Stochastic Analysis 2006 (12 juillet 2006) : 1–27. http://dx.doi.org/10.1155/jamsa/2006/95203.

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We present a unified approach to solving contracting problems with full information in models driven by Brownian motion. We apply the stochastic maximum principle to give necessary and sufficient conditions for contracts that implement the so-called first-best solution. The optimal contract is proportional to the difference between the underlying process controlled by the agent and a stochastic, state-contingent benchmark. Our methodology covers a number of frameworks considered in the existing literature. The main finance applications of this theory are optimal compensation of company executives and of portfolio managers.
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4

Ercolani, Joanne S. « CYCLICAL TRENDS IN CONTINUOUS TIME MODELS ». Econometric Theory 25, no 4 (août 2009) : 1112–19. http://dx.doi.org/10.1017/s0266466608090440.

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It is undoubtedly desirable that econometric models capture the dynamic behavior, like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, for instance, the cyclical growth models of Bergstrom (1966); the economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976); unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997); and differential-difference equations of Chambers and McGarry (2002). This paper considers continuous time cyclical trends, which complement the trend-plus-cycle models in the unobserved components literature but could also be incorporated into Bergstrom type systems of differential equations, as were stochastic trends in Bergstrom (1997).
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5

Knopov, P. S. « Some models of continuous-time stochastic approximation ». Cybernetics and Systems Analysis 31, no 6 (novembre 1995) : 863–68. http://dx.doi.org/10.1007/bf02366623.

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6

Wälde, Klaus. « Production technologies in stochastic continuous time models ». Journal of Economic Dynamics and Control 35, no 4 (avril 2011) : 616–22. http://dx.doi.org/10.1016/j.jedc.2010.10.005.

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7

Zipkin, Paul. « Stochastic leadtimes in continuous-time inventory models ». Naval Research Logistics Quarterly 33, no 4 (novembre 1986) : 763–74. http://dx.doi.org/10.1002/nav.3800330419.

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8

Bergstrom, A. R. « The History of Continuous-Time Econometric Models ». Econometric Theory 4, no 3 (décembre 1988) : 365–83. http://dx.doi.org/10.1017/s0266466600013359.

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Although it is only during the last decade that continuous-time models have been extensively used in applied econometric work, the development of statistical methods applicable to such models commenced over 40 years ago. The first significant contribution to the problem of estimating the parameters of continuous-time stochastic models from discrete data was made by the British statistician Bartlett [1946] only three years after the pioneering contribution of Haavelmo [1943] on simultaneous equations models. Moreover, by this time the fundamental mathematical theory of continuous-time stochastic models was already well developed, major contributions having been made by some of the leading mathematicians of the twentieth century, including Einstein, Weiner, and Kolmogorov.
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9

Pollock, D. Stephen G. « Linear Stochastic Models in Discrete and Continuous Time ». Econometrics 8, no 3 (4 septembre 2020) : 35. http://dx.doi.org/10.3390/econometrics8030035.

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The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [0,π] radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.
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10

Comte, Fabienne, et Eric Renault. « Long memory in continuous-time stochastic volatility models ». Mathematical Finance 8, no 4 (octobre 1998) : 291–323. http://dx.doi.org/10.1111/1467-9965.00057.

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11

Patterson, Richard L. « Continuous time stochastic compartmental models of discrete populations ». Mathematical and Computer Modelling 11 (1988) : 975–78. http://dx.doi.org/10.1016/0895-7177(88)90638-3.

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12

Fergusson, Kevin. « Forecasting inflation using univariate continuous‐time stochastic models ». Journal of Forecasting 39, no 1 (16 juillet 2019) : 37–46. http://dx.doi.org/10.1002/for.2603.

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13

Gong, H., et A. Thavaneswaran. « Recursive estimation for continuous time stochastic volatility models ». Applied Mathematics Letters 22, no 11 (novembre 2009) : 1770–74. http://dx.doi.org/10.1016/j.aml.2009.06.014.

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14

Harvey, A. C., et James H. Stock. « Continuous time autoregressive models with common stochastic trends ». Journal of Economic Dynamics and Control 12, no 2-3 (juin 1988) : 365–84. http://dx.doi.org/10.1016/0165-1889(88)90046-2.

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15

Krishnamurthy, Vikram, Elisabeth Leoff et Jörn Sass. « Filterbased stochastic volatility in continuous-time hidden Markov models ». Econometrics and Statistics 6 (avril 2018) : 1–21. http://dx.doi.org/10.1016/j.ecosta.2016.10.007.

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16

Bean, N. G., R. Elliott, A. Eshragh et J. V. Ross. « On Binomial Observations of Continuous-Time Markovian Population Models ». Journal of Applied Probability 52, no 2 (juin 2015) : 457–72. http://dx.doi.org/10.1239/jap/1437658609.

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In this paper we consider a class of stochastic processes based on binomial observations of continuous-time, Markovian population models. We derive the conditional probability mass function of the next binomial observation given a set of binomial observations. For this purpose, we first find the conditional probability mass function of the underlying continuous-time Markovian population model, given a set of binomial observations, by exploiting a conditional Bayes' theorem from filtering, and then use the law of total probability to find the former. This result paves the way for further study of the stochastic process introduced by the binomial observations. We utilize our results to show that binomial observations of the simple birth process are non-Markovian.
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17

Bean, N. G., R. Elliott, A. Eshragh et J. V. Ross. « On Binomial Observations of Continuous-Time Markovian Population Models ». Journal of Applied Probability 52, no 02 (juin 2015) : 457–72. http://dx.doi.org/10.1017/s0021900200012572.

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In this paper we consider a class of stochastic processes based on binomial observations of continuous-time, Markovian population models. We derive the conditional probability mass function of the next binomial observation given a set of binomial observations. For this purpose, we first find the conditional probability mass function of the underlying continuous-time Markovian population model, given a set of binomial observations, by exploiting a conditional Bayes' theorem from filtering, and then use the law of total probability to find the former. This result paves the way for further study of the stochastic process introduced by the binomial observations. We utilize our results to show that binomial observations of the simple birth process are non-Markovian.
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18

NIELSEN, JAN NYGAARD, et MARTIN VESTERGAARD. « ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS ». International Journal of Theoretical and Applied Finance 03, no 02 (avril 2000) : 279–308. http://dx.doi.org/10.1142/s0219024900000139.

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The stylized facts of stock prices, interest and exchange rates have led econometricians to propose stochastic volatility models in both discrete and continuous time. However, the volatility as a measure of economic uncertainty is not directly observable in the financial markets. The objective of the continuous-discrete filtering problem considered here is to obtain estimates of the stock price and, in particular, the volatility using discrete-time observations of the stock price. Furthermore, the nonlinear filter acts as an important part of a proposed method for maximum likelihood for estimating embedded parameters in stochastic differential equations. In general, only approximate solutions to the continuous-discrete filtering problem exist in the form of a set of ordinary differential equations for the mean and covariance of the state variables. In the present paper the small-sample properties of a second order filter is examined for some bivariate stochastic volatility models and the new combined parameter and state estimation method is applied to US stock market data.
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19

Bergstrom, A. R. « Optimal control in wide-sense stationary continuous-time stochastic models ». Journal of Economic Dynamics and Control 11, no 3 (septembre 1987) : 425–43. http://dx.doi.org/10.1016/s0165-1889(87)80016-7.

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20

Lin, Liang-Ching, Sangyeol Lee et Meihui Guo. « The Bickel–Rosenblatt test for continuous time stochastic volatility models ». TEST 23, no 1 (15 décembre 2013) : 195–218. http://dx.doi.org/10.1007/s11749-013-0347-1.

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21

Legault, Geoffrey, et Brett A. Melbourne. « Accounting for environmental change in continuous-time stochastic population models ». Theoretical Ecology 12, no 1 (5 juillet 2018) : 31–48. http://dx.doi.org/10.1007/s12080-018-0386-z.

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22

Saario, Vesa. « Comparison of the discrete and continuous- time stochastic selling models ». Engineering Costs and Production Economics 12, no 1-4 (juillet 1987) : 15–20. http://dx.doi.org/10.1016/0167-188x(87)90057-7.

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23

Sigman, Karl, et Reade Ryan. « Continuous-time monotone stochastic recursions and duality ». Advances in Applied Probability 32, no 2 (juin 2000) : 426–45. http://dx.doi.org/10.1239/aap/1013540172.

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A duality is presented for continuous-time, real-valued, monotone, stochastic recursions driven by processes with stationary increments. A given recursion defines the time evolution of a content process (such as a dam or queue), and it is shown that the existence of the content process implies the existence of a corresponding dual risk process that satisfies a dual recursion. The one-point probabilities for the content process are then shown to be related to the one-point probabilities of the risk process. In particular, it is shown that the steady-state probabilities for the content process are equivalent to the first passage time probabilities for the risk process. A number of applications are presented that flesh out the general theory. Examples include regulated processes with one or two barriers, storage models with general release rate, and jump and diffusion processes.
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24

Sigman, Karl, et Reade Ryan. « Continuous-time monotone stochastic recursions and duality ». Advances in Applied Probability 32, no 02 (juin 2000) : 426–45. http://dx.doi.org/10.1017/s0001867800010016.

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A duality is presented for continuous-time, real-valued, monotone, stochastic recursions driven by processes with stationary increments. A given recursion defines the time evolution of a content process (such as a dam or queue), and it is shown that the existence of the content process implies the existence of a corresponding dual risk process that satisfies a dual recursion. The one-point probabilities for the content process are then shown to be related to the one-point probabilities of the risk process. In particular, it is shown that the steady-state probabilities for the content process are equivalent to the first passage time probabilities for the risk process. A number of applications are presented that flesh out the general theory. Examples include regulated processes with one or two barriers, storage models with general release rate, and jump and diffusion processes.
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25

Mahata, Kaushik, et Minyue Fu. « ON THE RECONSTRUCTION OF CONTINUOUS-TIME MODELS FROM ESTIMATED DISCRETE-TIME MODELS OF STOCHASTIC PROCESSES ». IFAC Proceedings Volumes 39, no 1 (2006) : 422–27. http://dx.doi.org/10.3182/20060329-3-au-2901.00063.

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26

Chambers, Marcus J. « DISCRETE TIME REPRESENTATIONS OF COINTEGRATED CONTINUOUS TIME MODELS WITH MIXED SAMPLE DATA ». Econometric Theory 25, no 4 (août 2009) : 1030–49. http://dx.doi.org/10.1017/s0266466608090397.

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This paper derives an exact discrete time representation corresponding to a triangular cointegrated continuous time system with mixed stock and flow variables and observable stochastic trends. The discrete time model inherits the triangular structure of the underlying continuous time system and does not suffer from the apparent excess differencing that has been found in some related work. It can therefore serve as a basis for the study of the asymptotic sampling properties of estimators of the model's parameters. Some further analytical and computational results that enable Gaussian estimation to be implemented are also provided.
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27

Harvey, A. C., et James H. Stock. « The Estimation of Higher-Order Continuous Time Autoregressive Models ». Econometric Theory 1, no 1 (avril 1985) : 97–117. http://dx.doi.org/10.1017/s0266466600011026.

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A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables are subject to measurement error. The method is based on a state space representation and the use of the Kalman–Bucy filter. It is shown how the Kalman-Bucy filter can be modified to deal with flows as well as stocks.
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28

Bigi, S., T. Söderström et B. Carlsson. « An IV-Scheme for Estimating Continuous-Time Stochastic Models from Discrete-Time Data ». IFAC Proceedings Volumes 27, no 8 (juillet 1994) : 1561–66. http://dx.doi.org/10.1016/s1474-6670(17)47933-x.

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29

Jacod, Jean, Claudia Klüppelberg et Gernot Müller. « Functional Relationships Between Price and Volatility Jumps and Their Consequences for Discretely Observed Data ». Journal of Applied Probability 49, no 4 (décembre 2012) : 901–14. http://dx.doi.org/10.1239/jap/1354716647.

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Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein–Uhlenbeck and other continuous-time CARMA models as well as continuous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functionals of price and volatility processes for discrete observations of the price process on a grid, which are relevant for estimation and testing problems.
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Jacod, Jean, Claudia Klüppelberg et Gernot Müller. « Functional Relationships Between Price and Volatility Jumps and Their Consequences for Discretely Observed Data ». Journal of Applied Probability 49, no 04 (décembre 2012) : 901–14. http://dx.doi.org/10.1017/s0021900200012778.

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Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein–Uhlenbeck and other continuous-time CARMA models as well as continuous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functionals of price and volatility processes for discrete observations of the price process on a grid, which are relevant for estimation and testing problems.
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31

Ljung, Lennart, et Adrian Wills. « Issues in sampling and estimating continuous-time models with stochastic disturbances ». IFAC Proceedings Volumes 41, no 2 (2008) : 14360–65. http://dx.doi.org/10.3182/20080706-5-kr-1001.02433.

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32

NIELSEN, JAN NYGAARD, et MARTIN VESTERGAARD. « ERRATUM : "ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS" ». International Journal of Theoretical and Applied Finance 03, no 04 (octobre 2000) : 731. http://dx.doi.org/10.1142/s0219024900000772.

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33

Menoncin, Francesco, et Stefano Nembrini. « Stochastic continuous time growth models that allow for closed form solutions ». Journal of Economics 124, no 3 (12 septembre 2017) : 213–41. http://dx.doi.org/10.1007/s00712-017-0567-z.

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34

Ljung, Lennart, et Adrian Wills. « Issues in sampling and estimating continuous-time models with stochastic disturbances ». Automatica 46, no 5 (mai 2010) : 925–31. http://dx.doi.org/10.1016/j.automatica.2010.02.011.

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35

Blevins, Jason R. « IDENTIFYING RESTRICTIONS FOR FINITE PARAMETER CONTINUOUS TIME MODELS WITH DISCRETE TIME DATA ». Econometric Theory 33, no 3 (22 décembre 2015) : 739–54. http://dx.doi.org/10.1017/s0266466615000353.

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This paper revisits the question of parameter identification when a linear continuous time model is sampled only at equispaced points in time. Following the framework and assumptions of Phillips (1973), we consider models characterized by first-order, linear systems of stochastic differential equations and use a priori restrictions on the model parameters as identifying restrictions. A practical rank condition is derived to test whether any particular collection of at least $\left\lfloor {n/2} \right\rfloor$ general linear restrictions on the parameter matrix is sufficient for identification. We then consider extensions to incorporate prior restrictions on the covariance matrix of the disturbances, to identify the covariance matrix itself, and to address identification in models with cointegration.
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36

Gao, Jiti. « Modelling long-range-dependent Gaussian processes with application in continuous-time financial models ». Journal of Applied Probability 41, no 2 (juin 2004) : 467–82. http://dx.doi.org/10.1239/jap/1082999079.

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This paper considers a class of continuous-time long-range-dependent Gaussian processes. The corresponding spectral density is assumed to have a general and flexible form, which covers some important and special cases. For example, the spectral density of a continuous-time fractional stochastic differential equation is included. A modelling procedure is then established through estimating the parameters involved in the spectral density by using an extended continuous-time version of the Gauss–Whittle objective function. The resulting estimates are shown to be strongly consistent and asymptotically normal. An application of the modelling procedure to the identification and modelling of a fractional stochastic volatility is discussed in some detail.
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37

Gao, Jiti. « Modelling long-range-dependent Gaussian processes with application in continuous-time financial models ». Journal of Applied Probability 41, no 02 (juin 2004) : 467–82. http://dx.doi.org/10.1017/s0021900200014431.

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This paper considers a class of continuous-time long-range-dependent Gaussian processes. The corresponding spectral density is assumed to have a general and flexible form, which covers some important and special cases. For example, the spectral density of a continuous-time fractional stochastic differential equation is included. A modelling procedure is then established through estimating the parameters involved in the spectral density by using an extended continuous-time version of the Gauss–Whittle objective function. The resulting estimates are shown to be strongly consistent and asymptotically normal. An application of the modelling procedure to the identification and modelling of a fractional stochastic volatility is discussed in some detail.
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38

Sirignano, Justin, et Konstantinos Spiliopoulos. « Stochastic Gradient Descent in Continuous Time : A Central Limit Theorem ». Stochastic Systems 10, no 2 (juin 2020) : 124–51. http://dx.doi.org/10.1287/stsy.2019.0050.

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Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter updates occur in continuous time and satisfy a stochastic differential equation. This paper analyzes the asymptotic convergence rate of the SGDCT algorithm by proving a central limit theorem for strongly convex objective functions and, under slightly stronger conditions, for nonconvex objective functions as well. An [Formula: see text] convergence rate is also proven for the algorithm in the strongly convex case. The mathematical analysis lies at the intersection of stochastic analysis and statistical learning.
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39

Li, Yan, Tianliang Zhang, Xikui Liu et Xiushan Jiang. « Study onH-Index of Stochastic Linear Continuous-Time Systems ». Mathematical Problems in Engineering 2015 (2015) : 1–10. http://dx.doi.org/10.1155/2015/837053.

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This paper studies theH-index problem. We obtain a necessary and sufficient condition ofH-index larger thanγ>0. A generalized differential equation is introduced and it is proved that its solvability and the feasibility of theH-index are equivalent. We extend the deterministic cases to the stochastic models. Our results can be used to fault detection filter analysis. Finally, the effectiveness of the proposed results is illustrated by an example.
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40

Chan, Terence. « Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use ». ASTIN Bulletin 28, no 1 (mai 1998) : 77–93. http://dx.doi.org/10.2143/ast.28.1.519080.

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AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.
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41

Robinson, Peter M. « ON DISCRETE SAMPLING OF TIME-VARYING CONTINUOUS-TIME SYSTEMS ». Econometric Theory 25, no 4 (août 2009) : 985–94. http://dx.doi.org/10.1017/s0266466608090373.

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We consider a multivariate continuous-time process, generated by a system of linear stochastic differential equations, driven by white noise, and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a first-order model, but higher-order models are discussed in the case of equally-spaced observations. Some discussion of issues of statistical inference is included.
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42

Bezborodov, Viktor, Luca Di Persio, Tyll Krueger, Mykola Lebid et Tomasz Ożański. « Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes ». Advances in Applied Probability 50, no 01 (mars 2018) : 74–101. http://dx.doi.org/10.1017/apr.2018.5.

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AbstractWe formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar to the classical lattice growth models, the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free-branching birth rate.
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43

Boffi, Nicholas M., et Jean-Jacques E. Slotine. « A Continuous-Time Analysis of Distributed Stochastic Gradient ». Neural Computation 32, no 1 (janvier 2020) : 36–96. http://dx.doi.org/10.1162/neco_a_01248.

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We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing, where synchronization between agents is induced through communication with a common signal, we quantify how synchronization can significantly reduce the magnitude of the noise felt by the individual distributed agents and their spatial mean. This noise reduction is in turn associated with a reduction in the smoothing of the loss function imposed by the stochastic gradient approximation. Through simulations on model nonconvex objectives, we demonstrate that coupling can stabilize higher noise levels and improve convergence. We provide a convergence analysis for strongly convex functions by deriving a bound on the expected deviation of the spatial mean of the agents from the global minimizer for an algorithm based on quorum sensing, the same algorithm with momentum, and the elastic averaging SGD (EASGD) algorithm. We discuss extensions to new algorithms that allow each agent to broadcast its current measure of success and shape the collective computation accordingly. We supplement our theoretical analysis with numerical experiments on convolutional neural networks trained on the CIFAR-10 data set, where we note a surprising regularizing property of EASGD even when applied to the non-distributed case. This observation suggests alternative second-order in time algorithms for nondistributed optimization that are competitive with momentum methods.
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Eriksson, B., et M. R. Pistorius. « American Option Valuation under Continuous-Time Markov Chains ». Advances in Applied Probability 47, no 2 (juin 2015) : 378–401. http://dx.doi.org/10.1239/aap/1435236980.

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This paper is concerned with the solution of the optimal stopping problem associated to the value of American options driven by continuous-time Markov chains. The value-function of an American option in this setting is characterised as the unique solution (in a distributional sense) of a system of variational inequalities. Furthermore, with continuous and smooth fit principles not applicable in this discrete state-space setting, a novel explicit characterisation is provided of the optimal stopping boundary in terms of the generator of the underlying Markov chain. Subsequently, an algorithm is presented for the valuation of American options under Markov chain models. By application to a suitably chosen sequence of Markov chains, the algorithm provides an approximate valuation of an American option under a class of Markov models that includes diffusion models, exponential Lévy models, and stochastic differential equations driven by Lévy processes. Numerical experiments for a range of different models suggest that the approximation algorithm is flexible and accurate. A proof of convergence is also provided.
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45

Eriksson, B., et M. R. Pistorius. « American Option Valuation under Continuous-Time Markov Chains ». Advances in Applied Probability 47, no 02 (juin 2015) : 378–401. http://dx.doi.org/10.1017/s0001867800007904.

Texte intégral
Résumé :
This paper is concerned with the solution of the optimal stopping problem associated to the value of American options driven by continuous-time Markov chains. The value-function of an American option in this setting is characterised as the unique solution (in a distributional sense) of a system of variational inequalities. Furthermore, with continuous and smooth fit principles not applicable in this discrete state-space setting, a novel explicit characterisation is provided of the optimal stopping boundary in terms of the generator of the underlying Markov chain. Subsequently, an algorithm is presented for the valuation of American options under Markov chain models. By application to a suitably chosen sequence of Markov chains, the algorithm provides an approximate valuation of an American option under a class of Markov models that includes diffusion models, exponential Lévy models, and stochastic differential equations driven by Lévy processes. Numerical experiments for a range of different models suggest that the approximation algorithm is flexible and accurate. A proof of convergence is also provided.
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46

Koulis, Theodoro, Alexander Paseka et Aerambamoorthy Thavaneswaran. « Recursive Estimation for Continuous Time Stochastic Volatility Models Using the Milstein Approximation ». Journal of Mathematical Finance 03, no 03 (2013) : 357–65. http://dx.doi.org/10.4236/jmf.2013.33036.

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Wang, Zhengyan, Guanghua Xu, Peibiao Zhao et Zudi Lu. « The optimal cash holding models for stochastic cash management of continuous time ». Journal of Industrial & ; Management Optimization 14, no 1 (2018) : 1–17. http://dx.doi.org/10.3934/jimo.2017034.

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Turnovsky, Stephen J. « Applications of continuous-time stochastic methods to models of endogenous economic growth ». Annual Reviews in Control 20 (janvier 1996) : 155–66. http://dx.doi.org/10.1016/s1367-5788(97)00013-8.

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van Elburg, Ronald A. J. « Stochastic continuous time neurite branching models with tree and segment dependent rates ». Journal of Theoretical Biology 276, no 1 (mai 2011) : 159–73. http://dx.doi.org/10.1016/j.jtbi.2011.01.039.

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Turnovsky, S. « Applications of continuous-time stochastic methods to models of endogenous economic growth ». Annual Review in Automatic Programming 20 (1996) : 155–66. http://dx.doi.org/10.1016/s0066-4138(97)00013-x.

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