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 
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/
@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},
     year = {2005},
     volume = {8},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a3/}
}
TY  - JOUR
AU  - S. A. Gusev
TI  - Monte Carlo estimates of derivatives with respect to parameters of the solution of the parabolic equation based on numerical SDE solution
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2005
SP  - 297
EP  - 306
VL  - 8
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a3/
LA  - ru
ID  - SJVM_2005_8_4_a3
ER  - 
%0 Journal Article
%A S. A. Gusev
%T Monte Carlo estimates of derivatives with respect to parameters of the solution of the parabolic equation based on numerical SDE solution
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2005
%P 297-306
%V 8
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a3/
%G ru
%F SJVM_2005_8_4_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[2] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[3] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968 | MR | Zbl

[4] Gobet E., “Weak approximation of killed diffusion using Euler schemes”, Stochastic Processes and their Applications, 87 (2000), 167–197 | DOI | MR | Zbl

[5] Gusev S. A., “Estimation of the coefficients in the parabolic equation by the statistical simulation of diffusion trajectories”, Russ. J. Numer. Anal. Math. Modelling — VSP Publ., 18:4 (2003), 297–306 | DOI | MR

[6] Tikhonov V. I., Mironov V. A., Markovskie protsessy, Sovetskoe Radio, M., 1977 | MR | Zbl

[7] Averina T. A., Artemev S. S., Nekotorye voprosy postroeniya i ispolzovaniya chislennykh metodov dlya resheniya sistem stokhasticheskikh differentsialnykh uravnenii, Preprint / AN SSSR. Sib. otd-nie. VTs; 728, Novosibirsk, 1987 | MR

[8] Kramer G., Matematicheskie metody statistiki, Mir, M., 1975 | MR