scholarly journals On the stability of linear systems with delayed state defined over finite time interval

2002 ◽  
Author(s):  
D.Lj. Debeljkovic ◽  
S.A. Milinkovic ◽  
M.B. Jovanovic ◽  
Z.Lj. Nenadic
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
The Stability

SMOLUCHOWSKI–KRAMERS APPROXIMATION AND EXIT PROBLEMS

2005 ◽  
Vol 05 (04) ◽  
pp. 569-585 ◽  
Author(s):  
ZHIWEI CHEN ◽  
MARK FREIDLIN
Keyword(s):  
Large Deviations ◽  
Linear Systems ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Exit Problems

As is known, the solution of problem (1) converges to the solution of problem (3) uniformly on any finite time interval as μ ↓ 0. We study relations between large deviations for these two processes [Formula: see text] and [Formula: see text] as ε ↓ 0. A special attention is paid to the case of linear systems, when the quasi-potential is calculated explicitly.

STABILITY ANALYSIS OF DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT DELAY

2006 ◽  
Vol 16 (02) ◽  
pp. 465-472 ◽  
Author(s):  
WEIHUA DENG ◽  
YUJIANG WU ◽  
CHANGPIN LI
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Finite Time ◽  
Time Dependent ◽  
Time Interval ◽  
Finite Time Interval ◽  
Predator Prey ◽  
Gauss Type ◽  
Predator Prey Models ◽  
The Stability

In this Letter, we study the stability of differential equations with time-dependent delay. Several theorems are established for stability on a finite time interval, called "interval stability" for simplicity, and Liapunov stability. These theorems are applied to the generalized Gauss-type predator–prey models, and satisfactory results are obtained.

scholarly journals Regularization of inclusions of differential equations solutions based on the kinematics of a vector field in stability problems

2021 ◽  
Vol 2099 (1) ◽  
pp. 012045
Author(s):  
A N Rogalev
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Solution Sets ◽  
Strong Growth ◽  
System Parameters ◽  
The Stability

Abstract This paper presents the new results of computing the inclusions of sets of solutions of ordinary differential equations corresponding to perturbations acting on the solutions of the system. The regularization of algorithms for the inclusion of solutions is investigated. Inclusions of solutions are used to study the stability over a finite time interval under perturbations of the system parameters. The boundaries of solutions sets using methods that construct symbolic formulas that characterize the behavior of the system are computed. In this case, the Influence of permanent disturbances on the solutions is taken into account. It is proposed to use the parameters of the vector field of the problem in order to compensate for a strong growth of the computable solution boundaries, which is often encountered in many methods. This means the regularization of the problem of estimating inclusions of solution sets.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

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