scholarly journals Boundedness of one-dimensional branching Markov processes

1997 ◽  
Vol 10 (4) ◽  
pp. 307-332 ◽  
Author(s):  
F. I. Karpelevich ◽  
Yu. M. Suhov
Keyword(s):  
Markov Processes ◽  
Necessary Conditions ◽  
Random Variable ◽  
Expected Number ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
Type Boundary ◽  
The One ◽  
Branching Diffusions ◽  
Jump Markov Processes

A general model of a branching Markov process on ℝ is considered. Sufficient and necessary conditions are given for the random variable M=supt≥0max1≤k≤N(t)Ξk(t) to be finite. Here Ξk(t) is the position of the kth particle, and N(t) is the size of the population at time t. For some classes of processes (smooth branching diffusions with Feller-type boundary points), this results in a criterion stated in terms of the linear ODEσ2(x)2f″(x)+a(x)f′(x)=λ(x)(1−k(x))f(x). Here σ(x) and a(x) are the diffusion coefficient and the drift of the one-particle diffusion, respectively, and λ(x) and k(x) the intensity of branching and the expected number of offspring at point x, respectively. Similarly, for branching jump Markov processes the conditions are expressed in terms of the relations between the integral μ(x)∫π(x,dy)(f(y)−f(x)) and the product λ(x)(1−k(x))f(x), where λ(x) and k(x) are as before, μ(x) is the intensity of jumping at point x, and π(x,dy) is the distribution of the jump from x to y.

scholarly journals Moment Problems on Bounded and Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Quadratic Forms ◽  
Necessary Conditions ◽  
Unbounded Domains ◽  
Continuous Functions ◽  
Moment Problems ◽  
Two Dimensional ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
The One

Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional case. For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval. The latter result seems to give sufficient (and necessary) conditions for the existence of a multiplicative solution.

scholarly journals Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

scholarly journals The one-dimensional model for d-cones revisited

2016 ◽  
Vol 9 (3) ◽  
pp. 201-215 ◽  
Author(s):  
Heiner Olbermann
Keyword(s):  
Necessary Conditions ◽  
Energy Functional ◽  
Developable Surface ◽  
Dimensional Model ◽  
Bending Energy ◽  
Main Motivation ◽  
One Dimensional ◽  
Elastic Sheet ◽  
Physics Literature ◽  
The One

AbstractA d-cone is the shape one obtains when pushing an elastic sheet at its center into a hollow cylinder. In a simple model, one can treat the elastic sheet in the deformed configuration as a developable surface with a singularity at the “tip” of the cone. In this approximation, the renormalized elastic energy is given by the bending energy density integrated over some annulus in the reference configuration. The thus defined variational problem depends on the indentation ${{h}}$ of the sheet into the cylinder. This model has been investigated before in the physics literature; the main motivation for the present paper is to give a rigorous version of some of the results achieved there via formal arguments. We derive the Gamma-limit of the energy functional as ${{h}}$ is sent to 0. Furthermore, we analyze the minimizers of the limiting functional, and list a number of necessary conditions that they have to fulfill.

scholarly journals The existence of three positive solutions to integral type BVPs for singular second ODEs with one-dimensional p-Laplacian

2011 ◽  
Vol 27 (2) ◽  
pp. 239-248
Author(s):  
YUJI LIU ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Singular Differential Equations ◽  
One Dimensional ◽  
Type Boundary ◽  
The One

This paper is concerned with the integral type boundary value problems of the second order singular differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x 0 (t))]0 involved with the function ρ, which makes the solutions un-concave. Furthermore, f, g, h and ρ may be singular at t = 0 or t = 1.

Estimation of the integral of the square of derivatives of symmetric probability densities of one-dimensional random variables

Metrologiya ◽  
2020 ◽  
pp. 15-27
Author(s):  
Aleksandr V. Lapko ◽  
Vasiliy A. Lapko
Keyword(s):  
Standard Deviation ◽  
Probability Density ◽  
Random Variables ◽  
Random Variable ◽  
Density Estimates ◽  
One Dimensional ◽  
Probability Densities ◽  
The One ◽  
Derivatives Of ◽  
Selection Of

When substantiating the method of fast selection of the bandwidth of kernel probability density estimates, a constant was found that is a functional of the second density derivative. In this paper, the obtained result is generalized to derivatives of symmetric probability densities of different orders. The functional dependences of the constants under study on the coeffi cient of antikurtosis of a random variable are established. The regularities peculiar to them are investigated. Based on the results obtained, a method for estimating functionals from derived probability densities has been developed, which involves the following actions. In the original sample estimated standard deviation of the one-dimensional random variables and the coeffi cient of antikurtosis. Using the reconstructed functional dependences on the antikurtosis coeffi cient, the constants are estimated, which are functionals of the derivatives of the probability density. With known estimates of the standard deviation of the investigated random variable and the considered constant, the values of the functional from the derivative of the probability density of the selected order are calculated. The obtained results are confi rmed by the analysis of the data of computational experiments. It is established that with increasing order of the derivative, the values of the estimates of the studied functionals increase. This fact is explained by the complication of the integrand function in the considered functionals. The proposed method provides objective results for the fi rst three derivatives of the probability density of a random variable. The obtained conclusions are confi rmed by the results of the confi dence estimation of the investigated functionals.

scholarly journals A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY

Fractals ◽  
2004 ◽  
Vol 12 (03) ◽  
pp. 331-346 ◽  
Author(s):  
SERGIO BIANCHI
Keyword(s):  
Necessary Conditions ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Probability Distribution Functions ◽  
Self Similar ◽  
The One ◽  
New Distribution

In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

scholarly journals Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Integral Type ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Type Boundary ◽  
The One

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensionalp-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensionalp-Laplacian term[ρ(t)Φ(x’(t))]’involved with the functionρ, which makes the solutions un-concave.

A proof of the well posedness of discretized wave equation with an absorbing boundary condition

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
I. Alonso-Mallo ◽  
A.M. Portillo
Keyword(s):  
Wave Equation ◽  
Numerical Experiments ◽  
Necessary Conditions ◽  
Absorbing Boundary Conditions ◽  
Well Posedness ◽  
Initial Value ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
The One ◽  
Fifth Order

Abstract- Local absorbing boundary conditions with fifth order of absorption to approximate the solution of an initial value problem, for the spatially discretized wave equation, are considered. For the one dimensional case, it is proved necessary conditions for well posedness. Numerical experiments confirming well posedness and showing good results of absorption are included.

SOME NEW BOUNDS FOR THE RENEWAL FUNCTION

2006 ◽  
Vol 20 (2) ◽  
pp. 231-250 ◽  
Author(s):  
Konstadinos Politis ◽  
Markos V. Koutras
Keyword(s):  
Present Article ◽  
Lower Bounds ◽  
Upper Bound ◽  
Necessary Conditions ◽  
Lifetime Distribution ◽  
Specific Form ◽  
Renewal Function ◽  
Sufficient And Necessary Conditions ◽  
The One

In the literature, most of the bounds for the renewal function U(x) corresponding to a lifetime distribution F are given in terms of the first two moments of F only. The best general upper bound of this type is the one given in Lorden (1970). In the present article, we show that improved bounds can be obtained if one exploits the specific form of the distribution F. We derive a bound that improves upon Lorden's, at least on an interval [0,a) with a ≤ ∞, and we give both sufficient and necessary conditions for this improvement to hold uniformly for x ≥ 0. Refined upper as well as lower bounds are given for the case where F belongs to a class of distributions with monotone aging or when the renewal density is monotone.

scholarly journals SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR SINGULAR QUASI-LAPLACIAN DIFFERENTIAL EQUATIONS ON THE WHOLE LINE

2012 ◽  
Vol 17 (3) ◽  
pp. 423-446 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Continuous Operator ◽  
Completely Continuous ◽  
One Dimensional ◽  
Type Boundary ◽  
The One

This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the one-dimensional p-Laplacian term involving a nonnegative function ρ that may be singular at t = 0 and such that . A Banach space and a nonlinear completely continuous operator are defined in this paper. By using the Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established. An example is presented to illustrate the main theorem.

Sign in / Sign up

Export Citation Format

Share Document