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

• Autorzy: Aniello Fedullo , Vitalii Gasanenko
• Języki publikacji: EN

Abstrakty

EN

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 → ∞.

Słowa kluczowe

EN

Stochastic differential equations; solution of parabolic equations; eigenvalues problem; Poisson random measure; generating function; 60J60

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 4
• Strony: 624-634

Daty

wydano

2006-12-01

online

2006-12-01

Twórcy

autor

Aniello Fedullo

• Universita Degli Studi Di Salerno

autor

Vitalii Gasanenko

• National Academy of Science of Ukraine

Bibliografia

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

Identyfikatory

DOI

10.2478/s11533-006-0029-2