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Analysis of the archetypal functional equation in the noncritical case
P. 132141.

Language:
English
Keywords: марковские процессыMarkov processesharmonic functionspantograph equationгармонические функцииуравнения пантографа
Publication based on the results of:
Molchanov S., Bogachev L., Derfel G., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2015 Vol. 471 P. 119
Added: June 22, 2016
Alexeeva T., Shirokov N. A., Алгебра и анализ 2022 Т. 34 № 4 С. 121
We define Holder classes L^p_α(L) in the L^p(L) norm on a chordarc curve L in R^3 and prove direct and inverse approximation theorems for functions from these classes by functions harmonic in a neighborhood of the curve. The approximation is estimated in the L^p(L) norm, and the smaller the neighborhood, the more accurate the approximation. ...
Added: September 19, 2022
Kolokoltsov V., Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 3 P. 543600
This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Diﬀerential Equations of Caputo and RiemannLiouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to ...
Added: November 14, 2019
Manita A., , in : Analytical and Computational Methods in Probability Theory. Vol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin : Springer, 2017. P. 347360.
We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the centerofmass coordinate system. ...
Added: July 16, 2018
A.Manita, , in : Analytical and computational methods in probability theory and its applications (ACMPT2017). Proceedings of the International Scientific Conference. : M. : RUDN, 2017. P. 644648.
We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the centerofmass coordinate system. ...
Added: November 14, 2017
T. A. Alexeeva, N. A. Shirokov, Problemy Analiza 2019 Vol. 8(26) No. 3 P. 1623
Functional classes on a curve in a plane (a partial case of a spatial curve) can be described by the approximation speed by functions that are harmonic in threedimensional neighbourhoods of the curve. No constructive description of functional classes on rather general surfaces in R 3 and R 4 has been presented in literature so ...
Added: October 30, 2019
Landim C., Mariani M., Seo I., Archive for Rational Mechanics and Analysis 2019 Vol. 231 No. 2 P. 887938
We present two variational formulae for capacity in the context of nonselfadjoint elliptic operators. The minimizers of these variational problems are expressed as solutions of boundaryvalue elliptic equations. We use these principles to provide a sharp estimate for the transition times between two different wells for nonreversible diffusion processes. This estimate permits us to describe ...
Added: October 3, 2018
Olshanski G., , in : Probability and Statistical Physics in St. Petersburg. Vol. 91: Proceedings of Symposia in Pure Mathematics.: American Mathematical Society, 2016. P. 373394.
We discuss the construction of certain infinitedimensional continuous
time Markov processes, based on the use of intertwined Markov semigroups. ...
Added: February 21, 2017
Anatoly Manita, Queueing Systems 2014 Vol. 76 No. 2 P. 149180
We consider a stochastic model of clock synchronization in a wireless network of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales tN→∞ , N→∞ ...
Added: February 4, 2015
Tatyana A. Alexeeva, Nikolay A. Shirokov, Journal of Approximation Theory 2020 Vol. 249 Article 105308
Functional classes on a curve in a plane (a partial case
of a spatial curve) can be described by the approximation speed by
functions that are harmonic in threedimensional neighbourhoods
of the curve. No constructive description of functional classes on
rather general surfaces in R3 and R4 has been presented in literature
so far. The main result of the paper ...
Added: October 30, 2019
Kleptsyna M., Veretennikov A., Mathematical Methods of Statistics 2016 Vol. 25 No. 3 P. 207218
A new result on stability of an optimal nonlinear filter for a Markov chain with respect to small perturbations on every step is established. An exponential recurrence of the signal is assumed. ...
Added: October 16, 2016
Averboukh Y., SIAM Journal on Control and Optimization 2016 Vol. 54 No. 5 P. 26292649
The paper is concerned with a zerosum continuoustime stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied ...
Added: April 17, 2020
Olshanski G., Markov dynamics on the dual object to the infinitedimensional unitary group / Cornell University. Series math "arxiv.org". 2013. No. 1310.6155.
These are notes for a minicourse of 3 lectures given at the St. Petersburg
School in Probability and Statistical Physics (June 2012). My aim was to
explain, on the example of a particular model, how ideas from the
representation theory of big groups can be applied in probabilistic problems.
The material is based on the joint paper arXiv:1009.2029 by ...
Added: November 16, 2013
Borodin A., Olshanski G., Journal of Functional Analysis 2012 Vol. 263 P. 248303
We construct a fourparameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinitedimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinitedimensional unitary group U(∞). The process has a ...
Added: February 25, 2013
Olshanski G., Функциональный анализ и его приложения 2016 Т. 49 № 4 С. 6175
Ранее А. М. Бородин и автор построили 4параметрическое семейство марковских процессов на дуальном объекте к бесконечномерной унитарной группе. Основной новый результат состоит в том, что эти процессы являются пределами скачкообразных процессов на дуальных объектах к растущим компактным унитарным группам. ...
Added: December 29, 2016