Geodesic
Evaluation of expectation of a functionals depending on the solution of~linear stochastic equations
Trudy Instituta matematiki, Tome 22 (2014) no. 1, pp. 107-114.

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

The method for evaluation of expectation of a functionals depending on the solution of linear stochastic differential equations is proposed. This method is based on evaluation of the eigenvalues of a three-diagonal matrix using the Sturm sequences. It is considered the application of this method to evaluation of characteristics of Ising systems with random effect in the form of a random white noise process. 
@article{TIMB_2014_22_1_a8,
     author = {V. B. Malyutin},
     title = {Evaluation of expectation of a functionals depending on the solution of~linear stochastic equations},
     journal = {Trudy Instituta matematiki},
     pages = {107--114},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a8/}
}
TY  - JOUR
AU  - V. B. Malyutin
TI  - Evaluation of expectation of a functionals depending on the solution of~linear stochastic equations
JO  - Trudy Instituta matematiki
PY  - 2014
SP  - 107
EP  - 114
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a8/
LA  - ru
ID  - TIMB_2014_22_1_a8
ER  - 
%0 Journal Article
%A V. B. Malyutin
%T Evaluation of expectation of a functionals depending on the solution of~linear stochastic equations
%J Trudy Instituta matematiki
%D 2014
%P 107-114
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a8/
%G ru
%F TIMB_2014_22_1_a8
V. B. Malyutin. Evaluation of expectation of a functionals depending on the solution of~linear stochastic equations. Trudy Instituta matematiki, Tome 22 (2014) no. 1, pp. 107-114. http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a8/

[1] Kloeden P. E., Platen E., Numerical solution of stochastic differential equations, Springer-Verlag, 1992

[2] Kuznetsov D. F., Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, SPb., 2001

[3] Arato M., Linear stochastic systems with constant coefficients. A Statistical approach, Springer-Verlag, 1982

[4] Pugachev V. S., Sinitsyn I. N., Stochastic differential systems: Analisis and filtering, Wiley, New York, 1987

[5] Risken H., The Fokker–Planck equation. Methods of solution and applications, Springer-Verlag, 1984

[6] Egorov A. D., Zhidkov E. P., Lobanov Yu. Yu., Vvedenie v teoriyu i prilozheniya funktsionalnogo integrirovaniya, Fizmatlit, M., 2006

[7] Egorov A. D., Sabelfeld K., “Approximate formulas for expectations of functionals of solutions to stochastic differential equations”, Monte Carlo Methods and Applications, 18 (2009), 95–127

[8] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968

[9] Wilkinson J. H., The algebraic eigenvalue problem, Oxford, 1965

[10] Paladin G., Serva M., “Analytic solution of the random Ising model in one dimension”, Physical Review Letters, 69:5 (1992) | DOI

[11] Malyutin V. B., “Ob odnom metode vychisleniya funktsionalnykh integralov po spinovym peremennym”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2012, no. 3, 18–25