scholarly journals Testable forecasts

2021 ◽  
Vol 16 (1) ◽  
pp. 129-160
Author(s):  
Luciano Pomatto
Keyword(s):  
Stochastic Process ◽  
Hypothesis Testing ◽  
Adverse Selection ◽  
Recent Literature ◽  
Statistical Tests ◽  
Sufficient Conditions ◽  
Likelihood Ratio Tests ◽  
Selection Problems ◽  
Optimal Tests ◽  
Necessary And Sufficient

Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically. We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. This paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood‐ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman–Pearson paradigm of hypothesis testing.

Finite regular invariant measures for Feller processes

1968 ◽  
Vol 5 (1) ◽  
pp. 203-209 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Stochastic Process ◽  
Lyapunov Function ◽  
Invariant Measures ◽  
Sufficient Conditions ◽  
Ergodic Averages ◽  
Feller Process ◽  
The Third ◽  
Sequential Compactness ◽  
Finite Invariant Measure ◽  
Necessary And Sufficient

In the study of dynamical systems perturbed by noise, it is important to know whether the stochastic process of interest has a stationary distribution. Four necessary and sufficient conditions are formulated for the existence of a finite invariant measure for a Feller process on a σ-compact metric (state) space. These conditions link together stability notions from several fields. The first uses a Lyapunov function reminiscent of Lagrange stability in differential equations; the second depends on Prokhorov's condition for sequential compactness of measures; the third is a recurrence condition on the ergodic averages of the transition operator; and the fourth is analogous to a condition of Ulam and Oxtoby for the nonstochastic case.

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

2008 ◽  
Vol 464 (2095) ◽  
pp. 1761-1779 ◽  
Author(s):  
John A Quintanilla
Keyword(s):  
Random Media ◽  
Probability Function ◽  
Recent Literature ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Condition ◽  
Two Phase ◽  
Decomposition Formula ◽  
Positive Matrices ◽  
Necessary And Sufficient

Constructing realizations of random media with a specified two-point phase probability function S 2 has attracted considerable attention in the recent literature. However, little is known about conditions under which a prescribed S 2 is realizable. The only known necessary and sufficient condition, due to McMillan, involves a class of square matrices, called corner-positive matrices, about which almost nothing is known except their definition. As a result, McMillan's theorem has gone mostly unused in the literature for over 50 years. In this paper, we present a general decomposition formula for corner-positive matrices, which allows McMillan's theorem to be written in a significantly more tractable and testable form. We also connect McMillan's theorem with many known but heretofore unrelated necessary conditions on S 2 , extending many of these conditions.

scholarly journals A Predator–Prey Two-Sex Branching Process

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1408
Author(s):  
Cristina Gutiérrez ◽  
Carmen Minuesa
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Predator Population ◽  
Predator Prey ◽  
Control Functions ◽  
Branching Model ◽  
Necessary And Sufficient ◽  
Number Of Individuals ◽  
Random Control

In this paper, we present the first stochastic process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled branching model. This process is a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. In view of their potential for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them. Moreover, the description of the present predator–prey two-sex branching process on the fixation events can be performed in terms of the behaviour of a one-type two-sex branching process with a random control on the number of individuals, which is also introduced and analysed.

STOCHASTIC PROPERTIES OF DEGENERATED QUANTUM SYSTEMS

2010 ◽  
Vol 13 (01) ◽  
pp. 65-85 ◽  
Author(s):  
VSEVOLOD Zh. SAKBAEV
Keyword(s):  
Stochastic Process ◽  
Sufficient Conditions ◽  
Quantum Systems ◽  
Additive Measure ◽  
Divergent Sequence ◽  
Quantum Dynamical Semigroup ◽  
Dynamical Semigroup ◽  
The Family ◽  
Necessary And Sufficient ◽  
Stochastic Properties

We study Schrödinger equation with degenerated symmetric but not self-adjoint Hamiltonian. The above properties of the quantum Hamiltonian arise in the description of the asymptotic behavior of the regularizing self-adjoint Hamiltonians sequence. A quantum dynamical semigroup corresponding to degenerated Hamiltonian is defined by means of the passage to the limit for the sequence of the regularizing dynamical semigroups. These semigroups are generated by the regularizing self-adjoint Hamiltonians. The necessary and sufficient conditions are obtained for the convergence of the regularizing semigroups sequence. The description of the divergent sequence of semigroups requires the extension of the stochastic process concept. We extend the stochastic process concept onto the family of measurable functions defined on the space endowed with finite additive measure. The above extension makes it possible to describe the structure of the partial limits set of the regularizing semigroups sequence.

Finite regular invariant measures for Feller processes

1968 ◽  
Vol 5 (01) ◽  
pp. 203-209 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Stochastic Process ◽  
Lyapunov Function ◽  
Invariant Measures ◽  
Sufficient Conditions ◽  
Ergodic Averages ◽  
Feller Process ◽  
The Third ◽  
Sequential Compactness ◽  
Finite Invariant Measure ◽  
Necessary And Sufficient

In the study of dynamical systems perturbed by noise, it is important to know whether the stochastic process of interest has a stationary distribution. Four necessary and sufficient conditions are formulated for the existence of a finite invariant measure for a Feller process on a σ-compact metric (state) space. These conditions link together stability notions from several fields. The first uses a Lyapunov function reminiscent of Lagrange stability in differential equations; the second depends on Prokhorov's condition for sequential compactness of measures; the third is a recurrence condition on the ergodic averages of the transition operator; and the fourth is analogous to a condition of Ulam and Oxtoby for the nonstochastic case.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

Inventory optimization considering the vehicle capacity and specifics of cash flows at rental storage sites

2020 ◽  
pp. 77-90
Author(s):  
V.D. Gerami ◽  
I.G. Shidlovskii
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Sufficient Conditions ◽  
Cash Flows ◽  
Management Systems ◽  
Cargo Capacity ◽  
Special Modification ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Vehicle Capacity

The article presents a special modification of the EOQ formula and its application to the accounting of the cargo capacity factor for the relevant procedures for optimizing deliveries when renting storage facilities. The specified development will allow managers to take into account the following process specifics in the format of a simulated supply chain when managing inventory. First of all, it will allow considering the most important factor of cargo capacity when optimizing stocks. Moreover, this formula will make it possible to find the optimal strategy for the supply of goods if, also, it is necessary to take into account the combined effect of several factors necessary for practice, which will undoubtedly affect decision-making procedures. Here we are talking about the need for additional consideration of the following essential attributes of the simulated cash flow of the supply chain: 1) time value of money; 2) deferral of payment of the cost of the order; 3) pre-agreed allowable delays in the receipt of revenue from goods sold. Developed analysis and optimization procedures have been implemented to models of this type that are interesting and important for a business. This — inventory management systems, the format of which is related to the special concept of efficient supply. We are talking about models where the presence of the specified delays for the outgoing cash flows allows you to pay for the order and the corresponding costs of the supply chain from the corresponding revenue on the re-order interval. Accordingly, the necessary and sufficient conditions are established based on which managers will be able to identify models of the specified type. The purpose of the article is to draw the attention of managers to real opportunities to improve the efficiency of inventory management systems by taking into account these factors for a simulated supply chain.

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