Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: characteristic equation

Sortuj według:

Ogranicz wyniki do:

Necessary and sufficient conditions for oscillations of delay partial difference equations

100%

Zhang B., Liu S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1995

tom 15

nr 2

213-219

This paper is concerned with the delay partial difference equation (1) $A_{m+1,n}+A_{m,n+1}-A_{m,n} + Σ_{i=1}^u p_i A_{m-k_i, n-l_i} = 0$ where $p_i$ are real numbers, $k_i$ and $l_i$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

An asymptotic expansion for the distribution of the supremum of a random walk

63%

Sgibnev M. S.

Studia Mathematica

2000

tom 140

nr 1

41-55

Let ${S_n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of ${S_n}$ which takes into account the influence of the roots of the equation $1-∫_ℝe^{sx}F(dx)=0,F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Studia Mathematica

1 Liu S.

1 Sgibnev M. S.

1 Zhang B.

1 2000

1 1995

Wyniki wyszukiwania

Necessary and sufficient conditions for oscillations of delay partial difference equations

An asymptotic expansion for the distribution of the supremum of a random walk