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Of all publications in the section: 97
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Article
A.D. Manita. Theory of Probability and Its Applications. 2009. Vol. 53. No. 1. P. 155-161.

We consider a basic stochastic particle system consisting of N identical particles with isotropic k-particle synchronization, ${k\ge 2}$. In the limit when both the number of particles N and the time $t=t(N)$ grow to infinity we study an asymptotic behavior of a coordinate spread of the particle system. We describe three time stages of $t(N)$ for which a qualitative behavior of the system is completely different. Moreover, we discuss the case when a spread of the initial configuration depends on N and increases to infinity as $N\rightarrow\infty$.

Article
Bezhaeva Z., Oseledets V. I. Theory of Probability and Its Applications. 2013. Vol. 57. No. 1. P. 135-144.

The formula  for  calculating   the entropy and the Hausdorff   dimension of an  invariant   Erdos measure for the pseudogolden ratio and all values Bernoulli parameter   is obtained. This formula make possible calculating   the entropy and the Hausdorff   dimension  with high accuracy.

Article
Gushchin A. A. Theory of Probability and Its Applications. 2018. Vol. 62. No. 2. P. 216-235.

We characterize the set $W$ of possible joint laws of terminal values of a nonnegative submartingale $X$ of class $(D)$, starting at 0, and the predictable increasing process (compensator) from its Doob--Meyer decomposition. The set of possible values remains the same under certain additional constraints on $X$, for example, under the condition that $X$ is an increasing process or a squared martingale. Special attention is paid to extremal (in a certain sense) elements of the set $W$ and to the corresponding processes. We relate also our results with Rogers's results on the characterization of possible joint values of a martingale and its maximum.

Article
Kashtanov V. Theory of Probability and Its Applications. 2016. Vol. 60(2). P. 281-294.

We study the structure of the functional of accumulation defined on the trajectories of semi-Markov process with a finite set of states. As t -> ∞  this functional increases linearly and the coefficient is linear-fractional functional relative to the probability measure, defining homogeneous Markov randomized control strategy.

Article
Shur M. G. Theory of Probability and Its Applications. 2013. Vol. 57. No. 4. P. 659-662.
Article
Belkina T. A., Kabanov Y. Theory of Probability and Its Applications. 2016. Vol. 60. No. 4. P. 671-679.

We consider a model of an insurance company investing its reserve into a risky asset whose price follows a geometric Lévy process. We show that the nonruin probability is a viscosity solution of a second order integro-differential equation and prove a uniqueness theorem for the latter.

Article
Шур М. Г. Теория вероятностей и ее применения. 1990. Т. 35. № 4. С. 787-793.
Article
Пусев Р. С. Теория вероятностей и ее применения. 2010. Т. 55. № 1. С. 187-195.

We prove results on an exact small deviation asymptotics in L_2-norm for Matérn processes with arbitrary natural index and on logarithmic asymptotics for Matérn processes and fields with arbitrary indexes.

Article
Шур М. Г. Теория вероятностей и ее применения. 1995. Т. 40. № 2. С. 347-360.
Article
Шур М. Г. Теория вероятностей и ее применения. 1984. Т. 29. № 4. С. 692-702.
Article
Шур М. Г. Теория вероятностей и ее применения. 1985. Т. 30. № 2. С. 241-251.
Article
Житлухин М. В., Ширяев А. Н. Теория вероятностей и ее применения. 2012. Т. 57. № 3. С. 453-470.
Article
Жданов А. И., Питербарг В. И. Теория вероятностей и ее применения. 2018. Т. 63. № 1. С. 3-28.
Article
Шур М. Г. Теория вероятностей и ее применения. 2013. Т. 58. № 1. С. 200-205.
Article
Гущин А. А. Теория вероятностей и ее применения. 2010. Т. 55. № 4. С. 680-704.
Article
Житлухин М. В., Ширяев А. Н. Теория вероятностей и ее применения. 2013. Т. 58. № 1. С. 193-200.