basic lemma
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2021 ◽  
Vol 73 (8) ◽  
pp. 1056-1066
Author(s):  
A. Imomov ◽  
A. Meyliyev

UDC 519.218.2 We investigate an application of slowly varying functions (in sense of Karamata) in the theory of Markov branching processes. We treat the critical case so that the infinitesimal generating function of the process has the infinite second moment, but it regularly varies with the remainder. We improve the basic lemma of the theory of critical Markov branching processes and refine known limit results.


2016 ◽  
Vol 152 (6) ◽  
pp. 1237-1285 ◽  
Author(s):  
Florian Ivorra

Let $k=\mathbb{C}$ be the field of complex numbers. In this article we construct Hodge realization functors defined on the triangulated categories of étale motives with rational coefficients. Our construction extends to every smooth quasi-projective $k$-scheme, the construction done by Nori over a field, and relies on the original version of the basic lemma proved by Beĭlinson. As in the case considered by Nori, the realization functor factors through the bounded derived category of a perverse version of the Abelian category of Nori motives.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Azam A. Imomov

Consider the Markov Branching Process with continuous time. Our focus is on the limit properties of transition functions of this process. Using differential analogue of the Basic Lemma we prove local limit theorems for all cases and observe invariant properties of considering process.


Author(s):  
Paul Munro ◽  
Hannu Toivonen ◽  
Geoffrey I. Webb ◽  
Wray Buntine ◽  
Peter Orbanz ◽  
...  
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