scholarly journals Quasi-Feller Markov chains

2000 ◽  
Vol 13 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Jean B. Lasserre
Keyword(s):  
Probability Measure ◽  
Asymptotic Properties ◽  
Invariant Probability Measure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Strong Feller Property ◽  
Feller Property ◽  
Occupation Measures ◽  
Necessary And Sufficient ◽  
Strong Feller

We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong) Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong) Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.

scholarly journals Dynamical properties of some adic systems with arbitrary orderings

2016 ◽  
Vol 37 (7) ◽  
pp. 2131-2162 ◽  
Author(s):  
SARAH FRICK ◽  
KARL PETERSEN ◽  
SANDI SHIELDS
Keyword(s):  
Probability Measure ◽  
Fixed Points ◽  
Invariant Probability Measure ◽  
Random Order ◽  
Periodic Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Weakly Mixing ◽  
Dynamical Properties ◽  
Necessary And Sufficient

We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli–Vershik) system, with a transformation that is defined on most of the space of infinite paths that begin at the root. We prove that for every ordering the coding of orbits according to the partition of the path space determined by the first three edges is essentially faithful, meaning that it is one-to-one on a set of paths that has full measure for every fully supported invariant probability measure. We also show that for every$k$the subshift that arises from coding orbits according to the first$k$edges is topologically weakly mixing. We give a necessary and sufficient condition for any adic system to be topologically conjugate to an odometer and use this condition to determine the probability that a random order on a fixed diagram, or a diagram constructed at random in some way, is topologically conjugate to an odometer. We also show that the closure of the union over all orderings of the subshifts arising from codings of the Pascal adic by the first edge has superpolynomial complexity, is not topologically transitive, and has no periodic points besides the two fixed points, while the intersection over all orderings consists of just four orbits.

scholarly journals A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS
Keyword(s):  
Limit Theorem ◽  
Dynamical Systems ◽  
Compact Group ◽  
Short Proof ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Occupation Measure ◽  
Necessary And Sufficient Condition ◽  
Occupation Measures ◽  
Necessary And Sufficient

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.

scholarly journals Some results on the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments

1982 ◽  
Vol 32 (3) ◽  
pp. 295-317 ◽  
Author(s):  
Ch. G. Philos ◽  
Y. G. Sficas ◽  
V. A. Staikos
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
General Setting ◽  
Nonoscillatory Solution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Image Position ◽  
Necessary And Sufficient

AbstractThis paper deals with some asymptotic properties of nonoscillatory solutions of a class of n-th order (n < 1) differential equations with deviationg arguments involving the so called n-th order r-derivative of the unknown function x defined bywhere ri (i = 0,1…n) are positive continous functions on [t0, ∞). The fundamental purpose of this paper is to find for any integer m, 0 < m < n – 1, a necessary and sufficient condition (depending on m) in order that three exists at least one (nonoscillatory) solution x so that the exists in R – {0} The results obtained extend some recent ones due to Philos (1978a) and they prove, in a general setting, the validity of a conjecture made by Kusano and Onose (1975).

scholarly journals DERIVATIVE FORMULA AND APPLICATIONS FOR HYPERDISSIPATIVE STOCHASTIC NAVIER–STOKES/BURGERS EQUATIONS

2012 ◽  
Vol 15 (03) ◽  
pp. 1250020 ◽  
Author(s):  
FENG-YU WANG ◽  
LIHU XU
Keyword(s):  
Invariant Probability Measure ◽  
Gradient Estimates ◽  
Navier Stokes ◽  
Markov Semigroup ◽  
Kernel Estimates ◽  
Strong Feller Property ◽  
Feller Property ◽  
Burgers Equations ◽  
Derivative Formula ◽  
Strong Feller

By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier–Stokes/Burgers equations. As applications, gradient estimates, dimension-free Harnack inequality, strong Feller property, heat kernel estimates and some properties of the invariant probability measure are derived.

scholarly journals Quasi-adjoint third order difference equations: oscillatory and asymptotic behavior

1986 ◽  
Vol 9 (4) ◽  
pp. 781-784 ◽  
Author(s):  
B. Smith
Keyword(s):  
Asymptotic Behavior ◽  
Adjoint Equation ◽  
Asymptotic Properties ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Oscillatory Solutions ◽  
Order Difference ◽  
Necessary And Sufficient

In this paper, asymptotic properties of solutions ofΔ3Vn+Pn−1Vn+1=0          (E+)are investigated via the quasi-adjoint equationΔ3Un+PnUn+2=0.             (E−)A necessary and sufficient condition for the existence of oscillatory solutions of(E+)is given. An example showing that it is possible for(E+)to have only nonoscillatory solutions is also given.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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