• Journal of applied mathematics & informatics
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• v.31 no.3_4
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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.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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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.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.619-631
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• 2000

We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.739-751
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• 2010

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

• Smart Structures and Systems
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• v.9 no.3
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• pp.231-251
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• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.677-683
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• 2003

In multi-allelic model $X\;=\;(x_1,\;x_2,\;\cdots\;,\;x_d),\;M_f(t)\;=\;f(p(t))\;-\;{\int_0}^t\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we examine the stochastic differential equation for model X and find the properties using stochastic differential equation.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.909-943
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• 2017

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).