Limit theorems for number of diffusion processes, which did not absorb by boundaries

Aniello Fedullo; Vitalii Gasanenko

Open Mathematics (2006)

  • Volume: 4, Issue: 4, page 624-634
  • ISSN: 2391-5455

Abstract

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We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.

How to cite

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Aniello Fedullo, and Vitalii Gasanenko. "Limit theorems for number of diffusion processes, which did not absorb by boundaries." Open Mathematics 4.4 (2006): 624-634. <http://eudml.org/doc/269258>.

@article{AnielloFedullo2006,
abstract = {We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.},
author = {Aniello Fedullo, Vitalii Gasanenko},
journal = {Open Mathematics},
keywords = {60J60},
language = {eng},
number = {4},
pages = {624-634},
title = {Limit theorems for number of diffusion processes, which did not absorb by boundaries},
url = {http://eudml.org/doc/269258},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Aniello Fedullo
AU - Vitalii Gasanenko
TI - Limit theorems for number of diffusion processes, which did not absorb by boundaries
JO - Open Mathematics
PY - 2006
VL - 4
IS - 4
SP - 624
EP - 634
AB - We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.
LA - eng
KW - 60J60
UR - http://eudml.org/doc/269258
ER -

References

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  1. [1] V.A. Gasanenko and A.B. Roitman: “Rarefaction of moving diffusion particles”, The Ukrainian Math. J., Vol. 56, (2004), pp. 691–694 Zbl1075.60066
  2. [2] I.I. Gikhman and A.V. Skorokhod: Introduction to the Theory of Random Processes, Nauka, Moscow, 1977, p. 568. 
  3. [3] O.A. Ladigenskaya, V.A. Solonnikov and N.N. Uraltseva: Linear and Quasilinearity Equations of Parabolic Type, Nauka, Moscow, 1963, p. 736. 
  4. [4] A. Fedullo and V.A. Gasanenko: “Limit theorems for rarefaction of set of diffusion processes by boundaries”, Theor. Stochastic Proc., Vol. 11(27), (2005), pp. 23–28. Zbl1142.60384
  5. [5] S.G. Mihlin: Partial Differential Linear Equations, Vyshaij shkola, Moscow, 1977, p. 431. 
  6. [6] A.N. Kolmogorov and S.V. Fomin: Elements of Theory of Functions and Functional Analysis, Nauka, Moscow, 1972, p. 496. 
  7. [7] L. Hörmander: The Analysis of Linear Partial Differential Operators III, Spinger-Verlag, 1985, p. 696. Zbl0601.35001
  8. [8] A.N. Tikhonov and A.A. Samarsky: The Equations of Mathematical Physics, Nauka, Moskow, 1977, p. 736. 
  9. [9] E. Janke, F. Emde and F. Losch: Special Functions, Nauka, Moskow, 1968, p. 344. 

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