scholarly journals On a Gauss-Kuzmin-Type Problem For a Generalized Gauss-Kuzmin Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Chrysoula Ganatsiou
Keyword(s):  
Probability Measure ◽  
Type Problem ◽  
Random System ◽  
Generalized Operator ◽  
Limit Probability ◽  
Special Case

A generalized limit probability measure associated with a random system with complete connections for a generalized Gauss-Kuzmin operator, only for a special case, is defined, and its behaviour is investigated. As a consequence a specific version of Gauss-Kuzmin-type problem for the above generalized operator is obtained.

scholarly journals Bayesian credibility premium with GB2 copulas

2020 ◽  
Vol 8 (1) ◽  
pp. 157-171 ◽  
Author(s):  
Himchan Jeong ◽  
Emiliano A. Valdez
Keyword(s):  
Probability Measure ◽  
Explicit Form ◽  
Insurance Premium ◽  
Response Variable ◽  
Generalized Pareto ◽  
Special Case ◽  
Change Of Probability Measure

AbstractFor observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.

scholarly journals A maximum principle for optimal control for a class of controlled systems

1996 ◽  
Vol 38 (2) ◽  
pp. 172-181
Author(s):  
Wensheng Xu
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Closed Loop ◽  
Point Boundary ◽  
Type Problem ◽  
Controlled Systems ◽  
Type Differential Equation ◽  
Special Case ◽  
Loop Form

AbstractApplying Ekeland's variational principle in this paper, we obtain a maximum principle for optimal control for a class of two-point boundary value controlled systems. The control domain need not be convex. For a special case, that is the so called LQ-type problem, we obtain the optimal control in the closed loop form and a corresponding Riccati type differential equation.

Simplex-valued probability

2010 ◽  
Vol 60 (5) ◽  
Author(s):  
Roman Frič
Keyword(s):  
Probability Theory ◽  
Probability Measure ◽  
Category Theory ◽  
Maximal Element ◽  
Unit Interval ◽  
Fuzzy Probability ◽  
First Case ◽  
Special Case ◽  
Generalized Probability ◽  
Fuzzy Probability Theory

AbstractWe continue our study of generalized probability from the viewpoint of category theory. Assuming that each generalized probability measure is a morphism, we model basic probabilistic notions within the category cogenerated by its range. It is known that the closed unit interval I = [0, 1], carrying a suitable difference structure, cogenerates the category ID in which the classical and fuzzy probability theories can be modeled. We study generalized probability theories modeled within two different categories cogenerated by a simplex S n = {(x 1, x 2, …, x n) ∈ I n: $$ \mathop \sum \limits_{i = 1}^n $$ x i ≤ 1}, carrying a suitable difference structure; since I and S 1 coincide, for n = 1 we get the fuzzy probability theory as a special case. In the first case, when the morphisms preserve the so-called pure elements, the resulting category S n D, n > 1, and ID are isomorphic and the generalized probability theories modeled in ID and S n D are “the same”. In the second case, when the morphisms map each maximal element to a maximal element, the resulting categories WS n D, n > 1, lead to different models of generalized probability theories. We define basic notions of the corresponding simplex-valued probability theories and mention some applications.

scholarly journals Stationary partitions and Palm probabilities

2006 ◽  
Vol 38 (3) ◽  
pp. 602-620 ◽  
Author(s):  
Günter Last
Keyword(s):  
Probability Measure ◽  
Voronoi Tessellation ◽  
Random Partition ◽  
Weighted Version ◽  
Stationary Point Process ◽  
Typical Cell ◽  
Palm Measure ◽  
Special Case ◽  
Palm Probabilities ◽  
Shift Coupling

A stationary partition based on a stationary point process N in ℝd is an ℝd-valued random field π={π(x): x∈ℝd} such that both π(y)∈N for each y∈ℝd and the random partition {{y∈ℝd: π(y)=x}: x∈N} is stationary jointly with N. Stationary partitions may be considered as general versions of the stationary random tessellations studied in stochastic geometry. As in the special case of the Voronoi tessellation, a stationary partition can be used to relate the underlying stationary probability measure to the associated Palm probability measure of N. In doing so, we will develop some basic theory for stationary partitions and extend properties of stationary tessellations to our more general case. One basic idea is that the stationary measure is (up to a shift) a weighted version of the Palm measure, where the weight is the volume of the typical cell. We will make systematic use of a known modified probability measure. Finally, we use our approach to extend some recent results on the shift coupling of the stationary distribution and the Palm distribution.

ONLINE LEARNING WITH MARKOV SAMPLING

2009 ◽  
Vol 07 (01) ◽  
pp. 87-113 ◽  
Author(s):  
STEVE SMALE ◽  
DING-XUAN ZHOU
Keyword(s):  
Markov Models ◽  
Measure Theory ◽  
Stochastic Matrix ◽  
Discrete Dynamical System ◽  
Theoretical Treatment ◽  
Axiom A ◽  
Push Forward ◽  
Finite Space ◽  
Limit Probability ◽  
Special Case

This paper attempts to give an extension of learning theory to a setting where the assumption of i.i.d. data is weakened by keeping the independence but abandoning the identical restriction. We hypothesize that a sequence of examples (xt, yt) in X × Y for t = 1, 2, 3,… is drawn from a probability distribution ρt on X × Y. The marginal probabilities on X are supposed to converge to a limit probability on X. Two main examples for this time process are discussed. The first is a stochastic one which in the special case of a finite space X is defined by a stochastic matrix and more generally by a stochastic kernel. The second is determined by an underlying discrete dynamical system on the space X. Our theoretical treatment requires that this dynamics be hyperbolic (or "Axiom A") which still permits a class of chaotic systems (with Sinai–Ruelle–Bowen attractors). Even in the case of a limit Dirac point probability, one needs the measure theory to be defined using Hölder spaces. Many implications of our work remain unexplored. These include, for example, the relation to Hidden Markov Models, as well as Markov Chain Monte Carlo methods. It seems reasonable that further work should consider the push forward of the process from X × Y by some kind of observable function to a data space.

scholarly journals Stationary partitions and Palm probabilities

2006 ◽  
Vol 38 (03) ◽  
pp. 602-620 ◽  
Author(s):  
Günter Last
Keyword(s):  
Probability Measure ◽  
Voronoi Tessellation ◽  
Random Partition ◽  
Weighted Version ◽  
Stationary Point Process ◽  
Typical Cell ◽  
Palm Measure ◽  
Special Case ◽  
Palm Probabilities ◽  
Shift Coupling

A stationary partition based on a stationary point process N in ℝ d is an ℝ d -valued random field π={π(x): x∈ℝ d } such that both π(y)∈N for each y∈ℝ d and the random partition {{y∈ℝ d : π(y)=x}: x∈N} is stationary jointly with N. Stationary partitions may be considered as general versions of the stationary random tessellations studied in stochastic geometry. As in the special case of the Voronoi tessellation, a stationary partition can be used to relate the underlying stationary probability measure to the associated Palm probability measure of N. In doing so, we will develop some basic theory for stationary partitions and extend properties of stationary tessellations to our more general case. One basic idea is that the stationary measure is (up to a shift) a weighted version of the Palm measure, where the weight is the volume of the typical cell. We will make systematic use of a known modified probability measure. Finally, we use our approach to extend some recent results on the shift coupling of the stationary distribution and the Palm distribution.

scholarly journals On a Gauss-Kuzmin type problem for piecewise fractional linear maps with explicit invariant measure

2000 ◽  
Vol 24 (11) ◽  
pp. 753-763 ◽  
Author(s):  
C. Ganatsiou
Keyword(s):  
Invariant Measure ◽  
Type Problem ◽  
Random System ◽  
Linear Map ◽  
Linear Maps ◽  
Ergodic Behaviour

A random system with complete connections associated with a piecewise fractional linear map with explicit invariant measure is defined and its ergodic behaviour is investigated. This allows us to obtain a variant of Gauss-Kuzmin type problem for the above linear map.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

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