Basic Lemma

2011 ◽  
pp. 73-73
Author(s):  
Paul Munro ◽  
Hannu Toivonen ◽  
Geoffrey I. Webb ◽  
Wray Buntine ◽  
Peter Orbanz ◽  
...  
Keyword(s):  
Basic Lemma

scholarly journals Limit Properties of Transition Functions of Continuous-Time Markov Branching Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Azam A. Imomov
Keyword(s):  
Continuous Time ◽  
Limit Theorems ◽  
Branching Process ◽  
Branching Processes ◽  
Local Limit ◽  
Markov Branching Process ◽  
Transition Functions ◽  
Basic Lemma ◽  
Invariant Properties ◽  
Local Limit Theorems

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.

scholarly journals On application of slowly varying functions with remainder in the theory of Markov branching processes with mean one and infinite variance

2021 ◽  
Vol 73 (8) ◽  
pp. 1056-1066
Author(s):  
A. Imomov ◽  
A. Meyliyev
Keyword(s):  
Generating Function ◽  
Critical Case ◽  
Branching Processes ◽  
Infinite Variance ◽  
Second Moment ◽  
Basic Lemma

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.

The Basic Lemma in Multiplicative Diophantine Analysis

1948 ◽  
Vol 32 (300) ◽  
pp. 182
Author(s):  
E. T. Bell
Keyword(s):  
Basic Lemma

scholarly journals Perverse, Hodge and motivic realizations of étale motives

2016 ◽  
Vol 152 (6) ◽  
pp. 1237-1285 ◽  
Author(s):  
Florian Ivorra
Keyword(s):  
Abelian Category ◽  
Derived Category ◽  
Original Version ◽  
Complex Numbers ◽  
Triangulated Categories ◽  
Basic Lemma

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.

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