The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (4) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfy λ0 = 0, λ j > 0 for each j > 0, and . Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λ j = jλ, µj = jμ) with catastrophes of several different types.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfy λ 0 = 0, λ j > 0 for each j > 0, and . Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λ j = jλ, µj = jμ) with catastrophes of several different types.

scholarly journals Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Mohammed Al-Refai ◽  
Muhammed Syam
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial Value ◽  
The Laplace Transform ◽  
Necessary And Sufficient

In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.

scholarly journals Weighted Exponential Inequalities

2001 ◽  
Vol 8 (1) ◽  
pp. 69-86
Author(s):  
H. P. Heinig ◽  
R. Kerman ◽  
M. Krbec
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Two Dimensions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Inequalities ◽  
Averaging Operator ◽  
The Laplace Transform ◽  
Discrete Analogues ◽  
Carleman’S Inequality ◽  
Necessary And Sufficient

Abstract Necessary and sufficient conditions on weight pairs are found for the validity of a class of weighted exponential inequalities involving certain classical operators. Among the operators considered are the Hardy averaging operator and its variants in one and two dimensions, as well as the Laplace transform. Discrete analogues yield characterizations of weighted forms of Carleman's inequality.

scholarly journals Laplace Transforms and Generalized Laguerre Polynomials

1958 ◽  
Vol 10 ◽  
pp. 177-182 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Laplace Transform ◽  
Laguerre Polynomials ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Representation Theorems ◽  
Generalized Laguerre Polynomials ◽  
Inversion Operator ◽  
The Laplace Transform ◽  
Necessary And Sufficient

Various sets of necessary and sufficient conditions are known in order that a function ƒ(s), analytic for Re s > 0, be represented as the Laplace transform of a function in L p(0,∞), 1 < p ⩽ ∞ . Most of these theories are based on the properties of some inversion operator for the transformation— see, for example, (7, chap. 7). However in the case p = 2 a number of representation theorems of a much simpler type are available.

Stochastic Orders in Terms of Laplace Transforms

1995 ◽  
Vol 45 (3-4) ◽  
pp. 195-202 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Orders ◽  
Partial Orderings ◽  
Life Distributions ◽  
Necessary And Sufficient

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

Some remarks on faster convergent infinite series

2012 ◽  
Vol 62 (4) ◽  
Author(s):  
Dušan Holý ◽  
Ladislav Matejíčka ◽  
Ľudovít Pinda
Keyword(s):  
Infinite Series ◽  
Sufficient Conditions ◽  
Convergent Series ◽  
Necessary And Sufficient Conditions ◽  
Convergence Criteria ◽  
Different Types ◽  
Necessary And Sufficient

AbstractA structure on terms of faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of faster convergent series with different types of terms are found. A faster convergence criteria for certain Kummer’s series is proved in this paper.

A Dam with seasonal input

1994 ◽  
Vol 31 (2) ◽  
pp. 526-541 ◽  
Author(s):  
Robert B. Lund
Keyword(s):  
Laplace Transform ◽  
Convergence Rates ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Stochastic Monotonicity ◽  
The Laplace Transform ◽  
Monotonicity Result ◽  
The Mean ◽  
The Moment ◽  
Necessary And Sufficient

This paper examines the infinitely high dam with seasonal (periodic) Lévy input under the unit release rule. We show that a periodic limiting distribution of dam content exists whenever the mean input over a seasonal cycle is less than 1. The Laplace transform of dam content at a finite time and the Laplace transform of the periodic limiting distribution are derived in terms of the probability of an empty dam. Necessary and sufficient conditions for the periodic limiting distribution to have finite moments are given. Convergence rates to the periodic limiting distribution are obtained from the moment results. Our methods of analysis lean heavily on the coupling method and a stochastic monotonicity result.

scholarly journals Convex sequences of higher order

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4655-4663
Author(s):  
Daniel Sofonea ◽  
Ioan Ţincu ◽  
Ana Acu
Keyword(s):  
Real Number ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Difference Operators ◽  
Real Sequence ◽  
Convex Sequence ◽  
Different Types ◽  
The Difference ◽  
Necessary And Sufficient

In this paper we study the class of convex sequences of higher order defined using the difference operators and investigate their properties. The notion of the convex sequence of order r ? N will be extended for r a real number. Some necessary and sufficient conditions such that a real sequence belongs to the class of convex sequences of higher order r ? R are introduced. Using different types of means we will investigate the convexity of higher order for real sequences.

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