On the Limit Behavior of Compositions of Measures in the Plane and Space of Lobachevsky

Tutubalin, V. N.

doi:10.1137/1107018

Cited by 20 publications

(5 citation statements)

References 2 publications

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“…Proof. Using the estimates from [19] (in the proof of [19, Lemma 1]) we conclude that there exist α > 0 and γ > 0 such that P (x, D(x, αt), t) ≤ C 1 (h)e −γt for all t ≥ 0.…”

Section: Examplesmentioning

confidence: 96%

General contact processes: inhomogeneous models, models on graphs and on manifolds

Pirogov,

Zhizhina

2021

Preprint

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The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant measures in the critical regime under the condition imposed on the associated Markov jump process. This condition, roughly speaking, requires the separation of any pair of trajectories of this jump process. The general scheme can be applied to the contact process on the lattice in a heterogeneous and random environments as well as to the contact process on graphs and on manifolds.

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“…Proof. Using the estimates from [19] (in the proof of [19, Lemma 1]) we conclude that there exist α > 0 and γ > 0 such that P (x, D(x, αt), t) ≤ C 1 (h)e −γt for all t ≥ 0.…”

Section: Examplesmentioning

confidence: 96%

General contact processes: inhomogeneous models, models on graphs and on manifolds

Pirogov,

Zhizhina

2021

Preprint

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“…The hyperbolic plane (also called the Lobachevsky plane) is a mathematical object that was linked to the theory of communication half a century ago [43,44,66,117,118]. In those modeling and analysis efforts, it was shown how noise due to random inhomogeneities in waveguides can be related to how a communication signal gets corrupted and how this is related to stochastic processes in the hyperbolic plane.…”

Section: Communications and Random Walks In The Hyperbolic Planementioning

confidence: 99%

“…where z 0 = r 0 e iθ0 ∈ H is arbitrary; that is, each choice of z 0 defines a different mapping from H to D. For the applications of these concepts to the analysis of waveguides with random inhomogeneities, see [43,44,66,90,117,118], and for more reading about the hyperbolic plane, see [109].…”

Section: The Groups Sl(2 R) and P Sl(2 R) And The Poincaré Half-plamentioning

confidence: 99%

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Chirikjian

2012

Applied and Numerical Harmonic Analysis

132

126

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“…A different but similar approach is due MOMENTS OF PROBABILITY MEASURES ON A GROUP 33 to V.N. Tutubalin [31]. Applications to the central limit theorem indicated already in [16] have been made precise 5y J. Faraut [6].…”

Section: H Heyermentioning

confidence: 99%

Moments of probability measures on a group

Heyer

1981

International Journal of Mathematics and Mathematical Sciences

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New developments and results in the theory of expectatiors and variances for random variables with range in a topological group are presented in the following order (i) Introduction (2) Basic notions (3) The three series theorem in Banach spaces (4) Moment Conditions (5) Expectations and variances (6) A general three series theorem (7) The special cases of finite groups and Lie groups (8)The strong laws of large numbers on a Lie group (9) Further studies on moments of probability measures

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On the Limit Behavior of Compositions of Measures in the Plane and Space of Lobachevsky

Cited by 20 publications

References 2 publications

General contact processes: inhomogeneous models, models on graphs and on manifolds

General contact processes: inhomogeneous models, models on graphs and on manifolds

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Moments of probability measures on a group

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