Geodesic
Monte Carlo estimates of derivatives with respect to parameters of the solution of the parabolic equation based on numerical~SDE solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 297-306

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In this paper, a statistical method of estimation of the solution of the parabolic equation and its derivatives with respect to parameters is proposed. This method is based on the numerical solution of stochastic differential equations (SDE's) by the Euler method. The order of convergence of using functionals of the SDE's is determined. Some numerical results are given. 
@article{SJVM_2005_8_4_a3,
     author = {S. A. Gusev},
     title = {Monte {Carlo} estimates of derivatives with respect to parameters of the solution of the parabolic equation based on {numerical~SDE} solution},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {297--306},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a3/}
}
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S. A. Gusev. Monte Carlo estimates of derivatives with respect to parameters of the solution of the parabolic equation based on numerical~SDE solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 297-306. http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a3/