1) Backward doubly stochastic differential equation (BDSDE)
重随机倒向随机微分方程
2) backward doubly stochastic differential equation
倒向重随机微分方程
1.
The comparison theorem of backward doubly stochastic differential equations with Poisson process(BDSDEP) can be obtained under Lipschitz condition by means of Gronwall inequality,Young inequality,and It formula,which means the solution increases with the coefficient and the terminal value of BDSDEP.
在Lipschitz条件下,利用Gronwall不等式、Young不等式和Ito^公式等,得到了带跳的倒向重随机微分方程解的比较定理,说明了带跳的倒向重随机微分方程的系数和终端值越大,其解越大。
3) backward doubly stochastic differential equations
倒向重随机微分方程
1.
Backward Doubly Stochastic Differential Equations under Non-Lipschitzian Coefficient;
非Lipschitz条件下的倒向重随机微分方程
2.
We establish a new connection between solutions of backward doubly stochastic differential equations(BDSDEs)on infinite horizon and the station-ary solutions of the SPDEs.
我们首次将无穷区间上的倒向重随机微分方程(BDSDE)的解与SPDE的平稳解联系起来。
3.
The comparison theorem of backward doubly stochastic differential equations(BDSDE) with jump can be obtained under non-Lipschitz condition by means of Gronwall inequality and Ito\'s formula.
研究了一类带跳的倒向重随机微分方程在非Lipschitz条件下的比较定理。
4) backward doubly stochastic differential equations
双重倒向随机微分方程
1.
Comparision theorem for multi-dimensional backward doubly stochastic differential equations;
多维双重倒向随机微分方程比较定理
5) forward-backward doubly stochastic differential equations
正倒向重随机微分方程
1.
The existence and uniqueness for the solution of forward-backward doubly stochastic differential equations were obtained under local Lipschitz condition,where the time duration could be arbitrarily given.
在局部Lipschitz条件下,得到了任意给定时间区间上,正倒向重随机微分方程解的存在惟一性结果。
2.
A general type of forward-backward doubly stochastic differential equations(FBDSDEs in short) was studied, which extends many important equations well studied before, including stochastic Hamiltonian systems.
研究了一类正倒向重随机微分方程,其涵盖了以前的包括随机Hamilton系统的很多情况。
6) backward stochastic differential equations
倒向随机微分方程
1.
Continuous dependence of the solution of multi-dimensional reflected backward stochastic differential equations on the parameters;
多维反射倒向随机微分方程的解对参数的连续依赖性
2.
A stability theorem of the solutions to backward stochastic differential equations under non-Lipschitz condition;
非Lipschitz条件下倒向随机微分方程解的稳定性
3.
The local and global existence and uniqueness are proved for the solution of Duffi-Epstein type backward stochastic differential equations with non-Lipschitz coefficients.
在系数满足一类非Lipschitz条件下证明了Duffie-Epstein框架下倒向随机微分方程的局部与整体解的存在唯一性并研究了解的稳定性问题。
补充资料：随机微分
随机微分
stochastic differential
厂(xr)一厂(戈!)+丁厂，(x.一)、x、+ 十告)/‘’‘戈一，“〔‘，‘“一、、入;仁厂“、，-一.厂(、一)一厂(x一)。x一夸/’，(、一)(。xN。二:.其中IX，X」是X的二次变差.【补注】乘积dX·dy更常写作武X，Y]，其中“方括号”〔X.Y}是一个具有限变差的过程，使得IX，川=戈y‘、+dX·dy(0，t].当X=Y时，得到二次变差【X，X】.它被用在本条末.实际上，它是概率二次变差:当X是标准Brown运动时，科X，XJ是玫比g口e测度，而轨道真实的二次变差几乎必然是无穷的.亦见半鞍〔s恻~m盯恤g渔le)，随机积分(sto-chastic integn幻);随机微分方程(stochasticd政化丈ltialeq飞‘ltlon). 对非平坦流形连续轨道随机过程的研究，伊藤随机微分是不方便的.因为伊藤公式(2)与联系着不同坐标系的通常微分规则不相容.使用Cll)aT~姻微分(S加tono访ch di挽rentjal)，可以得到一个与坐标无关的描述方法.见IAI]，【A2]，第5章，[A3]，以及。pa1DHO助，积分{Stm飞ono访ch云negnd).随机微分障记谧拓c di场，即山l;e1Oxac侧”ec以丽皿中-咖Pe.”H幼l 一种关于随机基(0，.厂，(.汽):，。，P)的半鞍类S中的每个过程X二(X。，气，尸)用公式 (dX)I=X，一Xl=(s，t」，定义的随机区间函数dX.在随机微分族ds二{dX:X〔必中用下面公式引人过程的加法(A)，过程的乘法(M)及乘积算子(P): (A)dX+dy=d(X+Y); (M)(，dX)(、。]一了:。dX(随机积分(stoch努tieintegral)，中是局部有界可料过程且适应于a域流(，，)，、、，)); (P)dX·dy=d(XY)一X_dy一Y_dX，其中X_和Y_是X和Y的左连续等价形. 由它得出 (dX·dy)(s，t」= 二1 .ip艺(戈一戈_.)( yt一y，_.)， {A{~0!二l其中△一(s=t。
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