A remark on positive sojourn times of symmetric processes

2018 ◽  
Vol 55 (1) ◽  
pp. 69-81
Author(s):  
Christophe Profeta
Keyword(s):  
Brownian Motion ◽  
Recurrence Relation ◽  
Lower Bounds ◽  
Sojourn Time ◽  
Occupation Time ◽  
Upper And Lower Bounds ◽  
Stable Processes ◽  
Two Dimensional ◽  
Symmetric Stable Processes ◽  
Sojourn Times

Abstract We show that under some slight assumptions, the positive sojourn time of a product of symmetric processes converges towards ½ as the number of processes increases. Monotony properties are then exhibited in the case of symmetric stable processes, and used, via a recurrence relation, to obtain upper and lower bounds on the moments of the occupation time (in the first and third quadrants) for two-dimensional Brownian motion. Explicit values are also given for the second and third moments in the n-dimensional Brownian case.

scholarly journals Brownian Motion and Harmonic Analysis on Sierpinski Carpets

1999 ◽  
Vol 51 (4) ◽  
pp. 673-744 ◽  
Author(s):  
Martin T. Barlow ◽  
Richard F. Bass
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Heat Kernel ◽  
Lower Bounds ◽  
Harnack Inequality ◽  
Harmonic Functions ◽  
Upper And Lower Bounds ◽  
Isotropic Diffusion ◽  
Sierpinski Carpets

AbstractWe consider a class of fractal subsets of d formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion X and determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.

SIGNATURE AND RELIABILITY OF CONDITIONAL THREE-DIMENSIONAL CONSECUTIVE-(s, s, s)-OUT-OF-(s, s, m):F SYSTEM

2014 ◽  
Vol 21 (02) ◽  
pp. 1450009 ◽  
Author(s):  
MADHURI G. KULKARNI ◽  
AKANKSHA S. KASHIKAR
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
System Failure ◽  
Three Dimension ◽  
Two Dimensional ◽  
Math Model ◽  
The Moment ◽  
Appl Math ◽  
F System

A three-dimensional consecutive (r1, r2, r3)-out-of-(m1, m2, m3):F system was introduced by Akiba et al. [J. Qual. Mainten. Eng.11(3) (2005) 254–266]. They computed upper and lower bounds on the reliability of this system. Habib et al. [Appl. Math. Model.34 (2010) 531–538] introduced a conditional type of two-dimensional consecutive-(r, s)-out-of-(m, n):F system, where the number of failed components in the system at the moment of system failure cannot be more than 2rs. We extend this concept to three dimension and introduce a conditional three-dimensional consecutive (s, s, s)-out-of-(s, s, m):F system. It is an arrangement of ms2 components like a cuboid and it fails if it contains either a cube of failed components of size (s, s, s) or 2s3 failed components. We derive an expression for the signature of this system and also obtain reliability of this system using system signature.

Aprioribounds for a class of nonlinear elliptic equations and applications to physical problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 75-81 ◽  
Author(s):  
Catherine Bandle
Keyword(s):  
Dirichlet Problem ◽  
Lower Bounds ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Nonlinear Dirichlet Problem ◽  
Nonlinear Elliptic ◽  
Physical Problems ◽  
Maximal Pressure

SynopsisUpper and lower bounds for the solutions of a nonlinear Dirichlet problem are given and isoperimetric inequalities for the maximal pressure of an ideal charged gas are constructed. The method used here is based on a geometrical result for two-dimensional abstract surfaces.

scholarly journals Upper and lower bounds of the first exit time of Brownian motion from The Minimum and Maximun Parabolic Domains with variable dimension to research the variation of biological species

2020 ◽  
Author(s):  
Chao Liu ◽  
Wenbin Che ◽  
Jingjun Zhang
Keyword(s):  
Brownian Motion ◽  
Lower Bounds ◽  
Exit Time ◽  
Biological Species ◽  
Integral Function ◽  
Upper And Lower Bounds ◽  
First Exit Time ◽  
Variable Dimension ◽  
First Time ◽  
Exact Constants

Abstract Consider a Brownian motion with variable dimension starting at an interior point of the minimum or maximum parabolic domains Dmax t and Dmin t in Rd(t)+2, d(t) ≥ 1 is an increasing integral function as t →∞,d(t) →∞, and let τDmax t and τDmin t denote the first time the Brownian motion exits from Dmax t and Dmin t , respectively. Upper and lower bounds with exact constants for the asymptotics of logP(τDmax t > t) and logP(τDmin t > t) are given as t → ∞, depending on the shape of the domain Dmax t and Dmin t . The methods of proof are based on Gordon’s inequality and early works of Li, Lifshits and Shi in the single general parabolic domain case.

scholarly journals Sojourn times for the Brownian motion

1998 ◽  
Vol 11 (3) ◽  
pp. 231-246 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Density Function ◽  
Sojourn Time ◽  
Brownian Motion Process ◽  
Explicit Formulas ◽  
Reflecting Brownian Motion ◽  
Sojourn Times ◽  
Motion Process

In this paper explicit formulas are given for the distribution function, the density function and the moments of the sojourn time for the reflecting Brownian motion process.

scholarly journals Spectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior

10.14311/1801 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Pavel Exner ◽  
Diana Barseghyan
Keyword(s):  
Spectral Analysis ◽  
Phase Space ◽  
Lower Bounds ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Critical Value ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Eigenvalue Bounds

In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when the allowed phase space is infinite but the operator still has a discrete spectrum. First we analyze two-dimensional operators with the potential |xy|p - ?(x2 + y2)p/(p+2)where p?1 and ??0. We show that there is a critical value of ? such that the spectrum for ??crit it is unbounded from below. In the subcriticalcase we prove upper and lower bounds for the eigenvalue sums. The second part of work is devoted toestimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions havinginfinite cusps which are geometrically nontrivial being either curved or twisted; we are going to showhow these geometric properties enter the eigenvalue bounds.

Equivalent Composite Laminated Beams With Various Elastic Constitutive Models

1999 ◽  
Author(s):  
Izhak Sheinman ◽  
Yeoshua Frostig
Keyword(s):  
Lower Bounds ◽  
Plane Stress ◽  
Constitutive Models ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Laminated Beams ◽  
Cylindrical Bending ◽  
One Dimensional ◽  
First Order ◽  
Shear Deformable

Abstract Equivalent one-dimensional constitutive models of composite laminated beams with shear deformation are derived from the classical laminate two-dimensional using first-order shear deformable theory. The present cylindrical bending constitutive models can be used — with much greater accuracy than their well known plane-strain and plane-stress counterparts — as upper and lower bounds, to one of which the behavior tends depending on the width-to-length ratio; this aspect was investigated and results are presented.

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