Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
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DOI：
10.1214/aop/1079021459
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发表时间：
2004
影响因子：
2.3
通讯作者：
M. Fuhrman;G. Tessitore
中科院分区：
文献类型：
--
作者：
M. Fuhrman;G. Tessitore
利用无穷维正、倒向随机发展方程，得到了无穷维空间中半线性椭圆型微分方程的解。后向方程被认为是一个无限的时间范围内，一个合适的增长条件取代了最终的条件。椭圆方程是在一个温和的意义上，也适用于最优控制的应用。最后，我们注意到，由于缺乏光滑性质，这里考虑的椭圆型偏微分方程不能用解析方法处理。
Solutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial differential equation considered here could not be treated by analytic methods.