scholarly journals On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 961
Author(s):  
Ekaterina Marova ◽  
Ekaterina Gromova ◽  
Polina Barsuk ◽  
Anastasia Shagushina
Keyword(s):  
Characteristic Function ◽  
Absorption Coefficient ◽  
Differential Game ◽  
Pollution Control ◽  
Characteristic Functions ◽  
Ecological Situation ◽  
The Real ◽  
Irkutsk Region ◽  
Function Construction

We consider various approaches for a characteristic function construction on the example of an n players differential game of pollution control with a prescribed duration. We explore the effect of the presence of an absorption coefficient in the game on characteristic functions. As an illustration, we consider a game in which the parameters are calculated based on the real ecological situation of the Irkutsk region. For this game, we compute a number of characteristic functions and compare their properties.

An inequality for characteristic functions

1972 ◽  
Vol 6 (1) ◽  
pp. 1-9 ◽  
Author(s):  
C.R. Heathcote ◽  
J.W. Pitman
Keyword(s):  
Positive Integer ◽  
Characteristic Function ◽  
Characteristic Functions ◽  
The Real ◽  
Powers Of 2

The paper is concerned with an extension of the inequality 1 - u(2nt) ≤ 4n[1-u(t)] for u(t) the real part of a characteristic function. The main result is that the inequality in fact holds for all positive integer n and not only powers of 2. Certain consequences are deduced and a brief discussion is given of the circumstances under which equality holds.

scholarly journals Superadditive extension of characteristic functions for cooperative differential games

2020 ◽  
Vol 12 (4) ◽  
pp. 40-61
Author(s):  
Екатерина Викторовна Громова ◽  
Ekaterina Gromova ◽  
Екатерина Марова ◽  
Ekaterina Marova
Keyword(s):  
Characteristic Function ◽  
Differential Games ◽  
Differential Game ◽  
Characteristic Functions ◽  
Cooperative Differential Games

The paper provides a constructive theorem that allows one to construct a superadditive characteristic function in a differential game based on a non-superadditive one. As an example, a differential game is considered in which the delta - and eta - characteristic functions are not superadditive. An additional construction is carried out and it is shown that the obtained functions satisfy superadditivity  

Recurrence for Markov processes on N lines

1971 ◽  
Vol 8 (04) ◽  
pp. 724-730
Author(s):  
Mark Pinsky
Keyword(s):  
Markov Process ◽  
Characteristic Function ◽  
Markov Processes ◽  
Real Line ◽  
Transition Function ◽  
Characteristic Functions ◽  
The Real ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Continuous Markov Process

Let Λ = R 1 × {1, 2, ···, N} denote N copies of the real line and ξ(t) = (X(t), α(t))be a right-continuous Markov process taking values in A having transition function of the form P(t, (x, α), A × {β}) = Fαβ (t, A – x). Fukushima and Hitsuda [2] have found the most general such transition function; the (matrix) logarithm of its characteristic function is decomposed into a Lévy-Khintchine integral on the diagonal and multiples of characteristic functions off the diagonal.

Relative stability, characteristic functions and stochastic compactness

1979 ◽  
Vol 28 (4) ◽  
pp. 499-509 ◽  
Author(s):  
R. A. Maller
Keyword(s):  
Distribution Function ◽  
Characteristic Function ◽  
Recent Result ◽  
Relative Stability ◽  
Domain Of Attraction ◽  
Characteristic Functions ◽  
Stability Characteristic ◽  
Stable Law ◽  
The Real ◽  
Stochastic Compactness

AbstractA recent result of Rogozin on the relative stability of a distribution function is extended, by giving equivalences for relative stability in terms of truncated moments of the distribution and in terms of the real and imaginary parts of the characteristic function. As an application, the known results on centering distributions in the domain of attraction of a stable law are extended to the case of stochastically compact distributions.

Recurrence for Markov processes on N lines

1971 ◽  
Vol 8 (4) ◽  
pp. 724-730
Author(s):  
Mark Pinsky
Keyword(s):  
Markov Process ◽  
Characteristic Function ◽  
Markov Processes ◽  
Real Line ◽  
Transition Function ◽  
Characteristic Functions ◽  
The Real ◽  
Matrix Logarithm ◽  
The Matrix ◽  
Continuous Markov Process

Let Λ = R1 × {1, 2, ···, N} denote N copies of the real line and ξ(t) = (X(t), α(t))be a right-continuous Markov process taking values in A having transition function of the form P(t, (x, α), A × {β}) = Fαβ(t, A – x). Fukushima and Hitsuda [2] have found the most general such transition function; the (matrix) logarithm of its characteristic function is decomposed into a Lévy-Khintchine integral on the diagonal and multiples of characteristic functions off the diagonal.

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

SOME EXTENSIONS OF A LEMMA OF KOTLARSKI

2012 ◽  
Vol 28 (4) ◽  
pp. 925-932 ◽  
Author(s):  
Kirill Evdokimov ◽  
Halbert White
Keyword(s):  
Characteristic Function ◽  
Characteristic Functions ◽  
Real Zeros ◽  
Number Of Zeros ◽  
Weaker Conditions

This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. In particular, the condition that the characteristic functions of M, U1, and U2 are nonvanishing can be replaced with much weaker conditions: The characteristic function of U1 can be allowed to have real zeros, as long as the derivative of its characteristic function at those points is not also zero; that of U2 can have an isolated number of zeros; and that of M need satisfy no restrictions on its zeros. We also show that Kotlarski’s lemma holds when the tails of U1 are no thicker than exponential, regardless of the zeros of the characteristic functions of U1, U2, or M.

Certain Fourier Transforms of Distributions: II

1954 ◽  
Vol 6 ◽  
pp. 186-189 ◽  
Author(s):  
Eugene Lukacs ◽  
Otto Szász
Keyword(s):  
Characteristic Function ◽  
Fourier Transforms ◽  
Necessary Conditions ◽  
Laplace Transforms ◽  
Characteristic Functions ◽  
Necessary Condition ◽  
Multiple Roots ◽  
Not Given ◽  
Class Of Functions

In an earlier paper (1), published in this journal, a necessary condition was given which the reciprocal of a polynomial without multiple roots must satisfy in order to be a characteristic function. This condition is, however, valid for a wider class of functions since it can be shown (2, theorem 2 and corollary to theorem 3) that it holds for all analytic characteristic functions. The proof given in (1) is elementary and has some methodological interest since it avoids the use of theorems on singularities of Laplace transforms. Moreover the method used in (1) yields some additional necessary conditions which were not given in (1) and which do not seem to follow easily from the properties of analytic characteristic functions.

Strong Time-Consistency of a Core: An Application to the Pollution Control Problem in Eastern Siberia

2021 ◽  
Author(s):  
Ekaterina V. Gromova ◽  
Polina I. Barsuk ◽  
Shimai Su
Keyword(s):  
Absorption Coefficient ◽  
Pollution Control ◽  
Time Consistency ◽  
Model Parameters ◽  
Eastern Siberia ◽  
Linear Quadratic ◽  
The Core ◽  
Consistency Property ◽  
Strong Time Consistency ◽  
The Russian Federation

In this paper, we study the (strong) time-consistency property of the core for a linear-quadratic differential game of pollution control with nonzero absorption coefficient and real values of the model parameters. The values of parameters are evaluated based on the data for the largest aluminum enterprises of Eastern Siberia region of the Russian Federation for the year 2016. The obtained results are accompanied with illustrations.

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