Finite state bilaterally deterministic strongly mixing processes

1996 ◽  
Vol 95 (1) ◽  
pp. 115-133 ◽  
Author(s):  
Robert M. Burton ◽  
Manfred Denker ◽  
Meir Smorodinsky
Keyword(s):  
Mixing Processes ◽  
Strongly Mixing ◽  
Finite State ◽  
Strongly Mixing Processes

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (4) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (04) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

MARKOV MATHEMATICAL MODEL OF DYNAMIC ADAPTIVE TESTING OF AN ACTIVE AGENT

2018 ◽  
pp. 29-35
Author(s):  
N. V. Brovka ◽  
P. P. Dyachuk ◽  
M. V. Noskov ◽  
I. P. Peregudova
Keyword(s):  
Mathematical Model ◽  
Finite State Machine ◽  
Active Agent ◽  
Adaptive Testing ◽  
State Machine ◽  
Learning Activities ◽  
Independent Learning ◽  
Complex Object ◽  
Total Reward ◽  
Finite State

The problem and the goal.The urgency of the problem of mathematical description of dynamic adaptive testing is due to the need to diagnose the cognitive abilities of students for independent learning activities. The goal of the article is to develop a Markov mathematical model of the interaction of an active agent (AA) with the Liquidator state machine, canceling incorrect actions, which will allow mathematically describe dynamic adaptive testing with an estimated feedback.The research methodologyconsists of an analysis of the results of research by domestic and foreign scientists on dynamic adaptive testing in education, namely: an activity approach that implements AA developmental problem-solving training; organizational and technological approach to managing the actions of AA in terms of evaluative feedback; Markow’s theory of cement and reinforcement learning.Results.On the basis of the theory of Markov processes, a Markov mathematical model of the interaction of an active agent with a finite state machine, canceling incorrect actions, was developed. This allows you to develop a model for diagnosing the procedural characteristics of students ‘learning activities, including: building axiograms of total reward for students’ actions; probability distribution of states of the solution of the problem of identifying elements of the structure of a complex object calculate the number of AA actions required to achieve the target state depending on the number of elements that need to be identified; construct a scatter plot of active agents by target states in space (R, k), where R is the total reward AA, k is the number of actions performed.Conclusion.Markov’s mathematical model of the interaction of an active agent with a finite state machine, canceling wrong actions allows you to design dynamic adaptive tests and diagnostics of changes in the procedural characteristics of educational activities. The results and conclusions allow to formulate the principles of dynamic adaptive testing based on the estimated feedback.

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