A bound for the remainder term in the asymptotic expansion of a functional constructed from a semi-Markov random evolution

2019 ◽  
Vol 98 ◽  
pp. 217-227
Author(s):  
V. S. Koroliuk ◽  
I. V. Samoilenko
Keyword(s):  
Asymptotic Expansion ◽  
Remainder Term ◽  
Random Evolution ◽  
Markov Random ◽  
Markov Random Evolution

Asymptotic expansion of a semi-Markov random evolution

2006 ◽  
Vol 58 (9) ◽  
pp. 1396-1414
Author(s):  
I. V. Samoilenko
Keyword(s):  
Asymptotic Expansion ◽  
Random Evolution ◽  
Markov Random ◽  
Markov Random Evolution

scholarly journals On the asymptotic expansion of the remainder term in the case of convergence to the Poisson law

1962 ◽  
Vol 2 (1) ◽  
pp. 35-48
Author(s):  
B. Grigelionis
Keyword(s):  
Asymptotic Expansion ◽  
Remainder Term ◽  
Poisson Law

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис, Об асимптотическом разложении остаточного члена в случае сходимости к закону Пуассона B. Grigelionis. Apie liekamojo nario asimptotinj išdėstymą konvergencijos į Puasono dėsnį atveju

Formulation and summation of hyperasymptotic expansions obtained from integrals

1998 ◽  
Vol 9 (2) ◽  
pp. 159-185
Author(s):  
J. G. B. BYATT-SMITH
Keyword(s):  
Asymptotic Expansion ◽  
Remainder Term ◽  
Exponentially Small

Formal hyperasymptotic expansions of integrals are obtained from the Poincaré asymptotic expansion by re-expanding the remainder term. We show that for the integrals under consideration these hyperasymptotic expansions can be made accurate to any desired exponentially-small order.

scholarly journals Error bounds for the asymptotic expansion of the Hurwitz zeta function

2017 ◽  
Vol 473 (2203) ◽  
pp. 20170363 ◽  
Author(s):  
G. Nemes
Keyword(s):  
Asymptotic Expansion ◽  
Zeta Function ◽  
Gamma Function ◽  
Error Bounds ◽  
Asymptotic Expansions ◽  
Remainder Term ◽  
Hurwitz Zeta Function ◽  
Polygamma Functions

In this paper, we reconsider the large- a asymptotic expansion of the Hurwitz zeta function ζ ( s , a ). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G -function and the s -derivative of the Hurwitz zeta function ζ ( s , a ) are provided. A detailed discussion on the sharpness of our error bounds is also given.

scholarly journals Asimptoticeskoe razlozenie dlja resenija neodnorodnogo raznostnogo uravnenija obscego vida

2015 ◽  
Vol 97 (111) ◽  
pp. 113-123
Author(s):  
M.S. Sgibnev
Keyword(s):  
Asymptotic Expansion ◽  
Difference Equation ◽  
Weight Function ◽  
Characteristic Equation ◽  
Remainder Term ◽  
General Type ◽  
Free Term ◽  
Integral Estimate

We obtain an asymptotic expansion for the solution of a nonhomogeneous difference equation of general type. The influence of the roots of the characteristic equation is taken into a count. An integral estimate with submultiplicative weight function is established for the remainder term depending on the existence of a corresponding submultiplicative moment of the free term of the equation.

scholarly journals Weak Convergence of Markov Random Evolutions in a Multidimensional Space

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Igor V. Samoilenko
Keyword(s):  
Weak Convergence ◽  
Singular Perturbation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Multidimensional Space ◽  
Random Evolution ◽  
Relative Compactness ◽  
Markov Random ◽  
Random Evolutions

We study Markov symmetrical and nonsymmetrical random evolutions in Rn. Weak convergence of Markov symmetrical random evolution to Wiener process and of Markov non-symmetrical random evolution to a diffusion process with drift is proved using problems of singular perturbation for the generators of evolutions. Relative compactness in DRn×Θ[0,∞) of the families of Markov random evolutions is also shown.

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