• Journal of the Korean Statistical Society
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• 제34권4호
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with 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 non-linear BSDE in two different cases.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.491-498
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• 2013

This note is concerned with the uniform $L^p$-continuity of solution for the stochastic differential equations under Lipschitz condition and linear growth condition. Furthermore, uniform $L^p$-continuity of the solution for the stochastic functional differential equation is given.

• 대한수학회보
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• 제57권2호
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• pp.311-330
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• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Structural Engineering and Mechanics
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• 제64권2호
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• 대한수학회보
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• 제56권2호
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• pp.479-489
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• 2019

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian sheet with Hurst parameters H, H' > 1/2, and a drift coefficient satisfying the linear growth condition. The result is obtained using a suitable Girsanov theorem for the fractional Brownian sheet.

• 대한수학회보
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• 제61권4호
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• pp.917-932
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• 2024

In this paper, we deal with the Euler-Maruyama (EM) scheme for stochastic differential equations driven by G-Brownian motion (G-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for G-SDEs are established.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• 호남수학학술지
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• 제45권3호
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• pp.433-456
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• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.