CAJ | 학술논문

经典的倒向随机微分方程以布朗运动做为干扰源，布朗运动是一种理想化的随机模型，从而使倒向随机微分方程的应用受到了限制。文中研究了以连续局部鞅为干扰源的倒向随机微分方程，在生成元满足一种非Lipschitz条件下，通过构造一个函数列的方法，利用Lebesgue's控制收敛定理和常微分方程的比较定理，证明了其解是存在的并且是唯一的，对经典的倒向随机微分方程进行了推广。
경전적도향수궤미분방정이포랑운동주위간우원，포랑운동시일충이상화적수궤모형，종이사도향수궤미분방정적응용수도료한제。문중연구료이련속국부앙위간우원적도향수궤미분방정，재생성원만족일충비Lipschitz조건하，통과구조일개함수렬적방법，이용Lebesgue's공제수렴정리화상미분방정적비교정리，증명료기해시존재적병차시유일적，대경전적도향수궤미분방정진행료추엄。
The classical backward stochastic differential equations (BSDE) theory is taken the Brownian motion as the noise source, but the Brown motion is one kind of extreme idealized model, which causes limitations of the BSDE theory in application. This paper studies the backward stochastic differential equation which is taken continuous local martingale as the noise source. The authors of the paper conclude a general existence and uniqueness of the solutions under non-Lipschitz condition on the generator by adopting the construction of function sequence, Lebesgue's dominated convergence theorem and the comparison of ordinary differential equation. The authors have also conducted a substantial extension of the classical backward stochastic differential equations.