Shchegolev A., Управление большими системами: сборник трудов 2023 № 102 С. 5–14
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are ...
Added: June 12, 2023
Marcati C., Rakhuba M., Schwab C., Advances in Computational Mathematics 2022 Vol. 48 No. 3 Article 18
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ3. We consider functions in countably normed Sobolev spaces with radial weights and analytic- or Gevrey-type control of weighted semi-norms. Several classes of boundary value and eigenvalue problems from science and engineering are discussed whose solutions belong to the ...
Added: October 30, 2022
Marcati C., Rakhuba M., Ulander J. ., Calcolo 2022 Article 2
We derive rank bounds on the quantized tensor train (QTT) compressed approximation of singularly perturbed reaction diffusion boundary value problems in one dimension. Specifically, we show that, independently of the scale of the singular perturbation parameter, a numerical solution with accuracy 0 < 𝜀 < 1 can be represented in the QTT format with a number of parameters that ...
Added: October 31, 2021
Aleksandr A. Shchegolev, Random Operators and Stochastic Equations 2022 Vol. 30 No. 3 P. 205–213
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition steps. An example of a class such a process provided indicates that such types of estimates considering several transition steps may ...
Added: October 30, 2021
Shchegolev A., Управление большими системами: сборник трудов 2021 № 90 С. 36–48
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the current probability distributions of the process apart from being dependent on the current state. Such processes often act as limits ...
Added: April 21, 2021
Marcati C., Rakhuba M., Christoph S., / Series math "arxiv.org". 2020.
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ3. We consider functions in countably normed Sobolev spaces with radial weights and analytic- or Gevrey-type control of weighted semi-norms. Several classes of boundary value and eigenvalue problems from science and engineering are discussed whose solutions belong to the countably ...
Added: October 20, 2020
Veretennikov A., Anulova S., Shcherbakov P., , in: Proc. 52nd IEEE Conference on Decision and Control, December 10-13, Florence, Italy, 2013.: Florence: IEEE, 2013. P. 1217–1222.
For degenerate mechanical systems with switching exponential convergence to the stationary regime has been established. ...
Added: October 18, 2014
Veretennikov A., Anulova S., , in: Modern Stochastics and ApplicationsVol. Springer, Optimization and Its Applications.: Springer, 2014. P. 159–174.
For degenerate Hybrid Stochastic Systems with full Dependence of all components exponential convergence to the stationary regime has been established. ...
Added: October 18, 2014