scholarly journals Markov sequence of carryover fuel resources

2019 ◽  
pp. 181-196 ◽  
Author(s):  
Elena Gubiy ◽  
◽  
Valery Zorkaltsev ◽  
Keyword(s):  
Markov Sequence

On the ordered partial sums of real random variables

1977 ◽  
Vol 14 (1) ◽  
pp. 75-88 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Variables ◽  
Partial Sums ◽  
Markov Sequence ◽  
Stieltjes Transforms ◽  
Independent And Identically Distributed

In 1952 Pollaczek discovered a remarkable formula for the Laplace-Stieltjes transforms of the distributions of the ordered partial sums for a sequence of independent and identically distributed real random variables. In this paper Pollaczek's result is proved in a simple way and is extended for a semi-Markov sequence of real random variables.

scholarly journals A Forward Algorithm for Solving Optimal Stopping Problems

2006 ◽  
Vol 43 (01) ◽  
pp. 102-113
Author(s):  
Albrecht Irle
Keyword(s):  
State Space ◽  
Optimal Stopping ◽  
Stopping Time ◽  
The State ◽  
Optimal Stopping Problem ◽  
Forward Algorithm ◽  
Optimal Stopping Time ◽  
Entrance Time ◽  
Markov Sequence ◽  
Optimal Stopping Problems

We consider the optimal stopping problem for g(Z n ), where Z n , n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B 0 ⊇ B 1 ⊇ B 2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.

Dependent thinning of point processes

1980 ◽  
Vol 17 (04) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Sums and weighted sums of a gamma Markov sequence

1988 ◽  
Vol 25 (01) ◽  
pp. 204-209 ◽  
Author(s):  
Ravindra M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Random Variables ◽  
Laplace Transforms ◽  
Weighted Sums ◽  
Sums Of Random Variables ◽  
Markov Sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

scholarly journals The Markov Chain of Energy Carryover Reserves in Models of Power Supply Reliability in Remote

2019 ◽  
Vol 114 ◽  
pp. 03004
Author(s):  
Elena Gubiy
Keyword(s):  
Energy Supply ◽  
Energy Demand ◽  
Sufficient Conditions ◽  
Supply System ◽  
Energy Sources ◽  
Energy Supply System ◽  
Nested Models ◽  
Markov Sequence ◽  
Upper Level ◽  
Supply Reliability

We consider mathematical models for analyzing the energy supply reliability of isolated systems and propose a three-level complex of nested models. The lower level represents the model of functioning of the energy supply system during the period under review. The second level is a model of the energy supply reliability analysis. This analysis is based on multiple simulations of functioning of the energy supply system in randomly formed conditions. The energy sources demand and supply, as well as the amount of carryover reserves of energy in storage, are assumed to be random values. To simulate functioning, the values of energy demand and production are formed using the Monto-Carlo method following their laws of probability. The random value of the carryover reserves is formed using the algorithm that generates the Markov sequence of these reserves. The upper level is represented by the model for selecting the optimal composition of the means ensuring reliability, i.e. energy reserves in the energy production and storage capacity. It was revealed that the algorithm for generating the random value of the energy sources carryover reserves yields the homogenous Markov sequence. Sufficient conditions for uniqueness of the stationary state were determined. Based on the experimental calculations, we estimated the number of iterations required to reach the stationary ergodic state.

Note on the reversible counters system of Lampard

1974 ◽  
Vol 11 (3) ◽  
pp. 624-628 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Branching Processes ◽  
Poisson Processes ◽  
Time Interval ◽  
Input Process ◽  
Markov Sequence ◽  
The Times ◽  
Bivariate Poisson Process

The paper considers an extension to the reversible counters system of Lampard [1]. In Lampard's model the input processes are two independent Poisson processes; this results in a gamma Markov sequence for the time-interval between successive output pulses and a negative binomial Markov sequence for the counts at the times of out-put pulses. We consider the input process to be a bivariate Poisson process and show that the first out-put process given above is not affected, while the second out-put-process becomes of a type studied in the theory of branching processes.

Dependent thinning of point processes

1980 ◽  
Vol 17 (4) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Unscented Kalman Filtering for Nonlinear Systems with Colored Measurement Noises and One-Step Randomly Delayed Measurements

2019 ◽  
Vol 23 (2) ◽  
pp. 165-174
Author(s):  
Xinmei Wang ◽  
Zhenzhu Liu ◽  
Feng Liu ◽  
Wei Liu ◽  
◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Kalman Filtering ◽  
Sampling Method ◽  
Unscented Transformation ◽  
Markov Sequence ◽  
One Step ◽  
Delayed Measurements ◽  
Measurement Noises ◽  
Symmetric Sampling ◽  
Filtering Problem

Traditional unscented Kalman filtering (UKF) cannot solve the filtering problem for nonlinear systems with colored measurement noises and one-step randomly delayed measurements. To fix this problem, a new UKF algorithm is proposed in this paper. First, a system model with one-step randomly delayed measurements and colored measurement noises is established, wherein a first order Markov sequence model for whitening colored noises and an independently identical distributed Bernoulli variable for modeling one-step randomly delayed measurements is introduced. Second, an UKF is proposed for the above established models through unscented transformation by calculating the nonlinear states posterior mean and covariance based on the Bayesian filter framework. Specially, the proportional symmetric sampling method is used in the new UKF algorithm. Finally, the effectiveness and superiority of the proposed method is verified via simulation.

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