Geodesic
Estimates of the parameters in system of stochastic differential equations with linear inclusion of parameters
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 1-11 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we give the method of calculating the maximum-likelihood estimates of the parameters in nonlinear system of stochastic differential equations, when unknown parameters are linearly included in the right-hand side of system. Maximum-likelihood function is constructed on the basis of the Euler scheme, that describes the discrete observations of the solution to equations system. We set the conditions to attain the maximum by the likelihood function. Estimates of the parameters are calculated by the iterative method. We consider the special cases of equations and give examples of calculations. 
@article{SJVM_1999_2_1_a0,
     author = {S. S. Artem'ev and M. A. Yakunin},
     title = {Estimates of the parameters in system of stochastic differential equations with linear inclusion of parameters},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {1--11},
     year = {1999},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a0/}
}
TY  - JOUR
AU  - S. S. Artem'ev
AU  - M. A. Yakunin
TI  - Estimates of the parameters in system of stochastic differential equations with linear inclusion of parameters
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1999
SP  - 1
EP  - 11
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a0/
LA  - ru
ID  - SJVM_1999_2_1_a0
ER  - 
%0 Journal Article
%A S. S. Artem'ev
%A M. A. Yakunin
%T Estimates of the parameters in system of stochastic differential equations with linear inclusion of parameters
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1999
%P 1-11
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a0/
%G ru
%F SJVM_1999_2_1_a0
S. S. Artem'ev; M. A. Yakunin. Estimates of the parameters in system of stochastic differential equations with linear inclusion of parameters. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a0/

[1] Tikhonov V. I., Mironov M. A., Markovskie protsessy, Sov. radio, M., 1977 | MR | Zbl

[2] Kazakov I. E., Gladkov D. I., Metody optimizatsii stokhasticheskikh sistem, Nauka, M., 1987 | MR

[3] Zuev S. M., Statisticheskoe otsenivanie parametrov matematicheskikh modelei zabolevanii, Nauka, M., 1988 | MR

[4] Duffie D., Dynamic Asset Pricing Theory, Princeton Univ. Press, Princeton, 1992

[5] Artemev S. S., Mikhailichenko I. G., Sinitsyn I. N., Statisticheskoe modelirovanie srochnykh finansovykh operatsii, RAN. Sib. otd-nie. VTs, Novosibirsk, 1997

[6] Yakunin M. A., “Otsenivanie parametrov mnogomernogo protsessa Ornshteina–Ulenbeka”, Teoriya i prilozheniya statisticheskogo modelirovaniya, AN SSSR. Sib. otd.-nie. VTs, Novosibirsk, 1988, 124–134 | MR

[7] Artemiev S. S., Yakunin M. A., “Estimation of the parameters in stochastic differential equations”, Russ. J. Numer. Anal. Math. Modelling, 12:1 (1997), 1–12 | DOI | MR | Zbl

[8] Borovkov A. A., Matematicheskaya statistika. Otsenka parametrov. Proverka gipotez, Nauka, M., 1984 | MR

[9] Anderson T. W., Olkin I., “Maximum-likelihood estimation of the parameters of a multivariate normal distribution”, Linear Algebra And Its Applications, 70 (1985), 147–171 | DOI | MR | Zbl

[10] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl

[11] Hull J., White A., “The pricing of options as assets with stochastic volatilities”, J. of Finance, 42 (1987), 281–300 | DOI

[12] Tikhonov V. I., Statisticheskaya radiotekhnika, Radio i svyaz, M., 1982