Numerical solution for a class of SPDEs over bounded domains
Numerical solution for a class of SPDEs over bounded domains
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DOI：
10.1080/17442508.2013.819510
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
D. Crisan;J. Xiong
中科院分区：
文献类型：
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作者：
D. Crisan;J. Xiong
带乘性噪声的抛物型随机偏微分方程在非线性滤波中起着重要作用。更确切地说，部分观测扩散的条件分布求解了这种类型方程的归一化版本。我们表明，一个可以近似的解决方案的SPDE的（未加权）经验措施的有限系统的相互作用粒子的情况下，扩散时，在一个紧凑的状态空间与反射边界的演变。这种近似与现有的近似不同，在现有的近似中，粒子被加权，并且粒子相互作用通过选择权重而不是在粒子运动的水平上产生，就像在这项工作中的情况一样。模拟粒子轨迹的随机微分方程系统由Pettersson [Stoch.过程Appl. 59（2）（1995），pp. 295-308]。
Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295–308].