Geodesic
A new sufficient condition for uniform integrability of exponential local martingales
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2020), pp. 5-13
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the article it is suggested a new sufficient condition for uniform integrability of continues exponential local martingales. It is shown that the condition is much weaker then a number of known sufficient conditions for uniform integrability of exponential local martingales.
Keywords: uniform integrability, exponential processes, stopping times
Mots-clés : martingales, martingales. 
@article{VTPMK_2020_3_a0,
     author = {D. Kh. Kazanchyan and V. M. Kruglov},
     title = {A new sufficient condition for uniform integrability of exponential local martingales},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--13},
     year = {2020},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2020_3_a0/}
}
TY  - JOUR
AU  - D. Kh. Kazanchyan
AU  - V. M. Kruglov
TI  - A new sufficient condition for uniform integrability of exponential local martingales
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2020
SP  - 5
EP  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2020_3_a0/
LA  - ru
ID  - VTPMK_2020_3_a0
ER  - 
%0 Journal Article
%A D. Kh. Kazanchyan
%A V. M. Kruglov
%T A new sufficient condition for uniform integrability of exponential local martingales
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2020
%P 5-13
%N 3
%U http://geodesic.mathdoc.fr/item/VTPMK_2020_3_a0/
%G ru
%F VTPMK_2020_3_a0
D. Kh. Kazanchyan; V. M. Kruglov. A new sufficient condition for uniform integrability of exponential local martingales. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2020), pp. 5-13. http://geodesic.mathdoc.fr/item/VTPMK_2020_3_a0/

[1] Cherny A., Shiryaev A., “On criteria for the uniform integrability of Brownian stochastic exponentials”, Optimal Control and Partial Differential Equations, eds. J.L. Menaldi et al., Iso Press, 2001, 1–13 | MR

[2] Chung K. L., Williams R. J., Introduction to stochastic Integration, Second Edition, Birkhauser, Boston, 1990 | MR | Zbl

[3] Girsanov I. V., “On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures”, Theory of Probability and its Applications, 5:3 (1960), 314–330 (in Russian) | MR

[4] Kazamaki N., Continuous Exponential Martingales and BMO, v. 1579, Lecture Notes in Mathematics, eds. A. Dold, B. Eckmann, F. Takens, Springer-Verlag, Berlin, Heidelberg, New York, 1994, 91 pp. | DOI | MR | Zbl

[5] Kazanchyan D. C., Kruglov V. M., “Uniform integrability of exponential processes”, Lobachevskii Journal of Mathematics, 40:10 (2019), 1498–1506 | DOI | MR | Zbl

[6] Klebaner F., Liptser R., “When a stochastic exponential is a true martingale. Extention of method of Bene's”, Theory of Probability and its Applications, 58:1 (2014), 38–62 | DOI | MR | MR | Zbl

[7] Krylov N. V., Introduction to the theory of diffusion processes, American Mathematical Society, Providence, 1995 | MR

[8] Medvegyev P., Stochastic Integration Theory, Oxford University Press, Oxford, 2007, 607 pp. | MR | Zbl

[9] Novikov A. A., “On an identity for stochastic integrals”, Theory of Probability and its Applications, 17:4 (1973), 717–720 | DOI | MR | Zbl

[10] Novikov A. A., “On the conditions of the uniform integrability of the continuous nonnegative martingales”, Theory of Probability and its Applications, 24:4 (1980), 820–824 | DOI | MR | Zbl | Zbl