scholarly journals A Generalized Telegraph Process with Velocity Driven by Random Trials

2013 ◽  
Vol 45 (04) ◽  
pp. 1111-1136 ◽  
Author(s):  
Irene Crimaldi ◽  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci
Keyword(s):  
Real Line ◽  
Counting Process ◽  
Bernoulli Trials ◽  
Exponential Distributions ◽  
The Real ◽  
Telegraph Process ◽  
Nonzero Mean ◽  
The Mean ◽  
Moving Particle ◽  
Random Trial

We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

scholarly journals A Generalized Telegraph Process with Velocity Driven by Random Trials

2013 ◽  
Vol 45 (4) ◽  
pp. 1111-1136 ◽  
Author(s):  
Irene Crimaldi ◽  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci
Keyword(s):  
Real Line ◽  
Counting Process ◽  
Bernoulli Trials ◽  
Exponential Distributions ◽  
The Real ◽  
Telegraph Process ◽  
Nonzero Mean ◽  
The Mean ◽  
Moving Particle ◽  
Random Trial

We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

Generalized Telegraph Process with Random Jumps

2013 ◽  
Vol 50 (02) ◽  
pp. 450-463 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci ◽  
Shelemyahu Zacks
Keyword(s):  
Real Line ◽  
Fixed Time ◽  
Exponential Distributions ◽  
Telegraph Process ◽  
Velocity Reversal ◽  
Alternating Renewal Process ◽  
Alternating Direction ◽  
Random Jumps ◽  
Random Times ◽  
Random Jump

We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at timet=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed timet, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

scholarly journals Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 22 ◽  
Author(s):  
Feliz Minhós
Keyword(s):  
Real Line ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Type Condition ◽  
The Real ◽  
Carathéodory Function ◽  
Mean Curvature Operator ◽  
The Mean ◽  
Autonomous Differential Equations ◽  
Laplacian Equations

In this paper, we consider the second order discontinuous differential equation in the real line, a t , u ϕ u ′ ′ = f t , u , u ′ , a . e . t ∈ R , u ( − ∞ ) = ν − , u ( + ∞ ) = ν + , with ϕ an increasing homeomorphism such that ϕ ( 0 ) = 0 and ϕ ( R ) = R , a ∈ C ( R 2 , R ) with a ( t , x ) > 0 for ( t , x ) ∈ R 2 , f : R 3 → R a L 1 -Carathéodory function and ν − , ν + ∈ R such that ν − < ν + . The existence and localization of heteroclinic connections is obtained assuming a Nagumo-type condition on the real line and without asymptotic conditions on the nonlinearities ϕ and f . To the best of our knowledge, this result is even new when ϕ ( y ) = y , that is for equation a t , u ( t ) u ′ ( t ) ′ = f t , u ( t ) , u ′ ( t ) , a . e . t ∈ R . Moreover, these results can be applied to classical and singular ϕ -Laplacian equations and to the mean curvature operator.

Approximation by entire functions in the mean on the real line

1991 ◽  
Vol 43 (1) ◽  
pp. 100-104 ◽  
Author(s):  
A. I. Stepanets ◽  
N. I. Stepanets
Keyword(s):  
Real Line ◽  
Entire Functions ◽  
The Real ◽  
The Mean

scholarly journals Generalized Telegraph Process with Random Jumps

2013 ◽  
Vol 50 (2) ◽  
pp. 450-463 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci ◽  
Shelemyahu Zacks
Keyword(s):  
Real Line ◽  
Fixed Time ◽  
Exponential Distributions ◽  
Telegraph Process ◽  
Velocity Reversal ◽  
Alternating Renewal Process ◽  
Alternating Direction ◽  
Random Jumps ◽  
Random Times ◽  
Random Jump

We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real

DERIVATION BASES ON THE REAL LINE (I)

1982 ◽  
Vol 8 (1) ◽  
pp. 67 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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