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Journal articles on the topic 'Linear Stochastic Differential Equations'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Buckdahn, Rainer. "Linear skorohod stochastic differential equations." Probability Theory and Related Fields 90, no. 2 (June 1991): 223–40. http://dx.doi.org/10.1007/bf01192163.

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2

Yong, Jiongmin. "Linear Forward—Backward Stochastic Differential Equations." Applied Mathematics and Optimization 39, no. 1 (January 2, 1999): 93–119. http://dx.doi.org/10.1007/s002459900100.

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3

Sykora, Henrik T., Daniel Bachrathy, and Gabor Stepan. "Stochastic semi‐discretization for linear stochastic delay differential equations." International Journal for Numerical Methods in Engineering 119, no. 9 (April 30, 2019): 879–98. http://dx.doi.org/10.1002/nme.6076.

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4

Español, Pep. "Stochastic differential equations for non-linear hydrodynamics." Physica A: Statistical Mechanics and its Applications 248, no. 1-2 (January 1998): 77–96. http://dx.doi.org/10.1016/s0378-4371(97)00461-5.

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5

Nguyen, Tien Dung. "LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS." Taiwanese Journal of Mathematics 17, no. 1 (January 2013): 333–50. http://dx.doi.org/10.11650/tjm.17.2013.1728.

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6

Arnold, Ludwig, and Peter Imkeller. "Rotation Numbers For Linear Stochastic Differential Equations." Annals of Probability 27, no. 1 (January 1999): 130–49. http://dx.doi.org/10.1214/aop/1022677256.

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7

Török, C. "Numerical solution of linear stochastic differential equations." Computers & Mathematics with Applications 27, no. 4 (February 1994): 1–10. http://dx.doi.org/10.1016/0898-1221(94)90050-7.

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8

Gy�ngy, I., and E. Pardoux. "On quasi-linear stochastic partial differential equations." Probability Theory and Related Fields 94, no. 4 (December 1993): 413–25. http://dx.doi.org/10.1007/bf01192556.

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9

Dabrowski, Jacek. "Parameter identification in linear stochastic differential equations." Statistics & Probability Letters 7, no. 5 (April 1989): 391–94. http://dx.doi.org/10.1016/0167-7152(89)90092-8.

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10

Buckdahn, R., and D. Nualart. "Linear stochastic differential equations and Wick products." Probability Theory and Related Fields 99, no. 4 (December 1994): 501–26. http://dx.doi.org/10.1007/bf01206230.

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11

Ocone, Daniel, and Etienne Pardoux. "Linear stochastic differential equations with boundary conditions." Probability Theory and Related Fields 82, no. 4 (1989): 489–526. http://dx.doi.org/10.1007/bf00341281.

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12

CONG, NGUYEN DINH. "LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 01, no. 01 (March 2001): 127–57. http://dx.doi.org/10.1142/s0219493701000084.

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We introduce a concept of Lyapunov exponents and Lyapunov spectrum for nonautonomous linear stochastic differential equations. The Lyapunov exponents are defined samplewise via the two-parameter flow generated by the equation. We prove that Lyapunov exponents are finite and nonrandom. Lyapunov exponents are used for investigation of Lyapunov regularity and stability of nonautonomous stochastic differential equations. The results show that the concept of Lyapunov exponents is still very fruitful for stochastic objects and gives us a useful tool for investigating sample stability as well as qualitative behavior of nonautonomous linear and nonlinear stochastic differential equations.
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13

Du, Kai, and Qi Zhang. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations." Stochastic Processes and their Applications 123, no. 5 (May 2013): 1616–37. http://dx.doi.org/10.1016/j.spa.2013.01.005.

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14

CONG, NGUYEN DINH, and STEFAN SIEGMUND. "DICHOTOMY SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 02, no. 02 (June 2002): 175–201. http://dx.doi.org/10.1142/s0219493702000364.

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We investigate a concept of dichotomy spectrum for nonautonomous linear stochastic differential equations, which is defined with sample-wise exponential dichotomy of the two-parameter flow generated by the equation. We use random norm and cohomology to capture the nature of the stochastic nonuniformity. The main result is our spectral theorem stating that the dichotomy spectrum consists of compact random intervals with corresponding spectral manifolds, which are Oseledets spaces if the equation generates a random dynamical system. The dichotomy spectrum is nonrandom and equals the Lyapunov spectrum if the stochastic differential equation is Lyapunov regular.
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15

Chen, Li, Zhen Wu, and Zhiyong Yu. "Delayed Stochastic Linear-Quadratic Control Problem and Related Applications." Journal of Applied Mathematics 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/835319.

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We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
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16

Fernando, B. P. W., and S. S. Sritharan. "Stochastic quasi-linear partial differential equations of evolution." Infinite Dimensional Analysis, Quantum Probability and Related Topics 18, no. 03 (September 2015): 1550021. http://dx.doi.org/10.1142/s0219025715500216.

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17

Boufoussi, Brahim, and Soufiane Mouchtabih. "Harnack-type inequality for linear fractional stochastic equations." Random Operators and Stochastic Equations 28, no. 4 (December 1, 2020): 281–90. http://dx.doi.org/10.1515/rose-2020-2046.

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AbstractUsing the coupling method and Girsanov theorem, we prove a Harnack-type inequality for a stochastic differential equation with non-Lipschitz drift and driven by a fractional Brownian motion with Hurst parameter {H<\frac{1}{2}}. We also investigate this inequality for a stochastic differential equation driven by an additive fractional Brownian sheet.
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18

Ferrante, Marco, and Aureli Alabert. "Linear stochastic differential equations with functional boundary conditions." Annals of Probability 31, no. 4 (October 2003): 2082–108. http://dx.doi.org/10.1214/aop/1068646379.

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19

Mamporia, B. "Linear Stochastic Differential Equations in a Banach Space." Theory of Probability & Its Applications 61, no. 2 (January 2017): 295–308. http://dx.doi.org/10.1137/s0040585x97t988150.

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20

Lim, Andrew E. B., and Xun Yu Zhou. "Linear-Quadratic Control of Backward Stochastic Differential Equations." SIAM Journal on Control and Optimization 40, no. 2 (January 2001): 450–74. http://dx.doi.org/10.1137/s0363012900374737.

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21

Mariela Ungureanu, Viorica. "Stochastic uniform observability of general linear differential equations." Dynamical Systems 23, no. 3 (September 2008): 333–50. http://dx.doi.org/10.1080/14689360802275773.

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22

POP-STOJANOVIĆ, Z. R. "Stochastic Differential Equations, Linear Filtering, and Chaos Expansion." Annals of the New York Academy of Sciences 706, no. 1 Stochastic Pr (December 1993): 8–12. http://dx.doi.org/10.1111/j.1749-6632.1993.tb24677.x.

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23

Alabert, Aureli, and Marco Ferrante. "Linear stochastic differential-algebraic equations with constant coefficients." Electronic Communications in Probability 11 (2006): 316–35. http://dx.doi.org/10.1214/ecp.v11-1236.

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24

Fujita, Yasuhiro. "Linear stochastic partial differential equations with constant coefficients." Journal of Mathematics of Kyoto University 28, no. 2 (1988): 301–10. http://dx.doi.org/10.1215/kjm/1250520483.

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25

Ma, Jin, and Jiongmin Yong. "On linear, degenerate backward stochastic partial differential equations." Probability Theory and Related Fields 113, no. 2 (February 23, 1999): 135–70. http://dx.doi.org/10.1007/s004400050205.

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26

Ünal, Gazanfer. "Stochastic symmetries of Wick type stochastic ordinary differential equations." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560079. http://dx.doi.org/10.1142/s2010194515600794.

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We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space [Formula: see text]. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in [Formula: see text] are obtained. A stochastic version of canonical variables is also introduced.
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27

Sun, Huiying, Meng Li, Shenglin Ji, and Long Yan. "Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/265621.

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We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ) differential games. A necessary and sufficient condition involved with the connection between stochasticTn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochasticTn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs). Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.
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28

GAWARECKI, L., V. MANDREKAR, and B. RAJEEV. "THE MONOTONICITY INEQUALITY FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 12, no. 04 (December 2009): 575–91. http://dx.doi.org/10.1142/s0219025709003902.

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We prove the monotonicity inequality for differential operators A and L that occur as coefficients in linear stochastic partial differential equations associated with finite-dimensional Itô processes. We characterize the solutions of such equations. A probabilistic representation is obtained for solutions to a class of evolution equations associated with time dependent, possibly degenerate, second-order elliptic differential operators.
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29

Cong, Nguyen Dinh, Luu Hoang Duc, and Phan Thanh Hong. "Lyapunov Spectrum of Nonautonomous Linear Young Differential Equations." Journal of Dynamics and Differential Equations 32, no. 4 (July 17, 2019): 1749–77. http://dx.doi.org/10.1007/s10884-019-09780-z.

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Abstract We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are regular in the sense of Lyapunov. In the stochastic setting, the system generates a stochastic two-parameter flow which satisfies the integrability condition, hence the Lyapunov exponents are random variables of finite moments. Finally, we prove a Millionshchikov theorem stating that almost all, in a sense of an invariant measure, linear nonautonomous Young differential equations are Lyapunov regular.
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30

Pulch, Roland. "Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations." Journal of Computational and Applied Mathematics 262 (May 2014): 281–91. http://dx.doi.org/10.1016/j.cam.2013.10.046.

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31

CONG, NGUYEN DINH. "ALMOST ALL NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS ARE REGULAR." Stochastics and Dynamics 04, no. 03 (September 2004): 351–71. http://dx.doi.org/10.1142/s0219493704001115.

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32

Kadiev, Ramazan, and Arcady Ponosov. "Input-to-State Stability of Linear Stochastic Functional Differential Equations." Journal of Function Spaces 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/8901563.

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The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “theW-method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown.
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33

Cuong, Dang Kien, Duong Ton Dam, Duong Ton Thai Duong, and Du Thuan Ngo. "Solutions to the jump-diffusion linear stochastic differential equations." Science and Technology Development Journal - Natural Sciences 3, no. 2 (September 6, 2019): 115–19. http://dx.doi.org/10.32508/stdjns.v3i2.663.

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The jump-diffusion stochastic process is one of the most common forms in reality (such as wave propagation, noise propagation, turbulent flow, etc.), and researchers often refer to them in models of random processes such as Wiener process, Levy process, Ito-Hermite process, in research of G. D. Nunno, B. Oksendal, F. B. Hanson, etc. In our research, we have reviewed and solved three problems: (1) Jump-diffusion process (also known as the Ito-Levy process); (2) Solve the differential equation jump-diffusion random linear, in the case of one-dimensional; (3) Calculate the Wiener-Ito integral to the random Ito-Hermite process. The main method for dealing with the problems in our presentation is the Ito random-integrable mathematical operations for the continuous random process associated with the arbitrary differential jump by the Poisson random measure. This study aims to analyse the basic properties of jump-diffusion process that are solutions to the jump-diffusion linear stochastic differential equations: dX(t) = [a (t)X (t􀀀)+A(t)]dt + [b (t)X (t􀀀 ∫ )+B(t)]dW (t) + R0 [g (t; z)X (t􀀀)+G(t; z)] ¯N (dt;dz) with a set of stochastic continuous functions fa;b ;g ;A;B;Gg and assuming that the compensated Poisson process ¯N (t; z) is independent of the Wiener process W(t). Derived from the Ito-Hermite formulas for the Ito-Hermite process and for the Ito-Levy process class we presented the results for the differential and multiple stochastic integration for the Ito- Hermite process. We also provided a separation method to solve jump-diffusion linear differential equations.
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34

Carbonell, F., and J. C. Jimenez. "Weak Local Linear Discretizations for Stochastic Differential Equations with Jumps." Journal of Applied Probability 45, no. 01 (March 2008): 201–10. http://dx.doi.org/10.1017/s002190020000406x.

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Weak local linear approximations have played a prominent role in the construction of effective inference methods and numerical integrators for stochastic differential equations. In this note two weak local linear approximations for stochastic differential equations with jumps are introduced as a generalization of previous ones. Their respective order of convergence is obtained as well.
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35

Carbonell, F., and J. C. Jimenez. "Weak Local Linear Discretizations for Stochastic Differential Equations with Jumps." Journal of Applied Probability 45, no. 1 (March 2008): 201–10. http://dx.doi.org/10.1239/jap/1208358962.

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Weak local linear approximations have played a prominent role in the construction of effective inference methods and numerical integrators for stochastic differential equations. In this note two weak local linear approximations for stochastic differential equations with jumps are introduced as a generalization of previous ones. Their respective order of convergence is obtained as well.
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36

Zhou, Haiying, Huainian Zhu, and Chengke Zhang. "Linear Quadratic Nash Differential Games of Stochastic Singular Systems." Journal of Systems Science and Information 2, no. 6 (December 25, 2014): 553–60. http://dx.doi.org/10.1515/jssi-2014-0553.

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AbstractIn this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.
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37

Paola, M. Di. "Linear Systems Excited by Polynomials of Filtered Poission Pulses." Journal of Applied Mechanics 64, no. 3 (September 1, 1997): 712–17. http://dx.doi.org/10.1115/1.2788955.

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The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equation that can be exactly solved.
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38

Fard, Omid S., and Ali V. Kamyad. "A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients." Journal of Applied Mathematics 2004, no. 6 (2004): 461–77. http://dx.doi.org/10.1155/s1110757x04401168.

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We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.
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39

RUPŠYS, PETRAS, and EDMUNDAS PETRAUSKAS. "ANALYSIS OF HEIGHT CURVES BY STOCHASTIC DIFFERENTIAL EQUATIONS." International Journal of Biomathematics 05, no. 05 (June 17, 2012): 1250045. http://dx.doi.org/10.1142/s1793524511001878.

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Height–diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the methodology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age–diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal copula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation methodology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine (Pinus sylvestris) trees provided the data for this study.
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40

Alili, Larbi, and Ching-Tang Wu. "Further results on some singular linear stochastic differential equations." Stochastic Processes and their Applications 119, no. 4 (April 2009): 1386–99. http://dx.doi.org/10.1016/j.spa.2008.07.004.

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41

Wang, Zhen, Xiong Li, and Jinzhi Lei. "Second moment boundedness of linear stochastic delay differential equations." Discrete & Continuous Dynamical Systems - B 19, no. 9 (2014): 2963–91. http://dx.doi.org/10.3934/dcdsb.2014.19.2963.

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42

Dareiotis, Konstantinos, and James-Michael Leahy. "Finite difference schemes for linear stochastic integro-differential equations." Stochastic Processes and their Applications 126, no. 10 (October 2016): 3202–34. http://dx.doi.org/10.1016/j.spa.2016.04.025.

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43

Buckdahn, R., P. Malliavin, and D. Nualart. "Multidimensional linear stochastic differential equations in the skorohod sense." Stochastics and Stochastic Reports 62, no. 1-2 (November 1997): 117–45. http://dx.doi.org/10.1080/17442509708834130.

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44

Jankunas, Andrius, and Rafail Z. Khasminskii. "Estimation of parameters of linear homogeneous stochastic differential equations." Stochastic Processes and their Applications 72, no. 2 (December 1997): 205–19. http://dx.doi.org/10.1016/s0304-4149(97)00083-5.

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45

Hofmann, Norbert, Thomas Müller-Gronbach, and Klaus Ritter. "Linear vs Standard Information for Scalar Stochastic Differential Equations." Journal of Complexity 18, no. 2 (June 2002): 394–414. http://dx.doi.org/10.1006/jcom.2001.0627.

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46

Rybunikova, T. S. "On Linear Row-Finite Systems of Stochastic Differential Equations." Theory of Probability & Its Applications 45, no. 3 (January 2001): 539–45. http://dx.doi.org/10.1137/s0040585x97978488.

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47

Al-Azzawi, Shahad Saadi Mahdi, Jicheng Liu, and Xianming Liu. "The synchronization of stochastic differential equations with linear noise." Stochastics and Dynamics 18, no. 06 (October 29, 2018): 1850049. http://dx.doi.org/10.1142/s0219493718500491.

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The synchronization of stochastic differential equations with both additive noise and linear multiplicative noise is investigated in pathwise sense, which generalize the results of [5] and [6]. In our situation, we can deal with the synchronization of the systems with mixed type noise, where one system has the additive noise, another has the linear multiplicative noise.
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48

Yong, Jiongmin. "Linear forward-backward stochastic differential equations with random coefficients." Probability Theory and Related Fields 135, no. 1 (July 14, 2005): 53–83. http://dx.doi.org/10.1007/s00440-005-0452-5.

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49

Potthoff, J., and G. Våge. "Generalized Solutions of Linear Parabolic Stochastic Partial Differential Equations." Applied Mathematics and Optimization 38, no. 1 (July 1, 1998): 95–107. http://dx.doi.org/10.1007/s002459900083.

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50

Hu, Ying, Jin Ma, and Jiongmin Yong. "On semi-linear degenerate backward stochastic partial differential equations." Probability Theory and Related Fields 123, no. 3 (July 1, 2002): 381–411. http://dx.doi.org/10.1007/s004400100193.

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