scholarly journals A discrete Stochastic Korovkin theorem

1991 ◽  
Vol 14 (4) ◽  
pp. 679-682
Author(s):  
George A. Anastassiou
Keyword(s):  
Stochastic Processes ◽  
State Space ◽  
Sufficient Condition ◽  
Korovkin Theorem ◽  
Index Set ◽  
Real State

In this article we give a sufficient condition for the pointwise−−in the first mean Korovkin property onB0(P), the space of stochastic processes with real state space and countable index setΓand bounded first moments.

Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

1987 ◽  
Vol 24 (02) ◽  
pp. 347-354 ◽  
Author(s):  
Guy Fayolle ◽  
Rudolph Iasnogorodski
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Stochastic Processes ◽  
State Space ◽  
Discrete Time ◽  
Random Variables ◽  
Countable State Space ◽  
Countable State ◽  
New Criteria

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn ), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn ) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

scholarly journals On Partial Complete Controllability of Semilinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Agamirza E. Bashirov ◽  
Maher Jneid
Keyword(s):  
Differential Equation ◽  
State Space ◽  
Control Systems ◽  
Order Differential Equation ◽  
Sufficient Condition ◽  
Complete Controllability ◽  
Semilinear Systems ◽  
First Order ◽  
Partial Controllability ◽  
First Order Differential Equations

Many control systems can be written as a first-order differential equation if the state space enlarged. Therefore, general conditions on controllability, stated for the first-order differential equations, are too strong for these systems. For such systems partial controllability concepts, which assume the original state space, are more suitable. In this paper, a sufficient condition for the partial complete controllability of semilinear control system is proved. The result is demonstrated through examples.

A Lyapunov Criterion for Invariant Probabilities with Geometric Tail

1998 ◽  
Vol 12 (3) ◽  
pp. 387-391
Author(s):  
Jean B. Lasserre
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Sufficient Condition ◽  
Countable State Space ◽  
Countable State

Given a Markov chain on a countable state space, we present a Lyapunov (sufficient) condition for existence of an invariant probability with a geometric tail.

scholarly journals Index-Based Notation for Random Variable and Probability Space

2019 ◽  
Vol 23 (4) ◽  
pp. 715-718 ◽  
Author(s):  
Hiroki Shibata ◽  
◽  
Yasufumi Takama
Keyword(s):  
State Space ◽  
Probability Space ◽  
Random Variables ◽  
Random Variable ◽  
Index Set ◽  
Conventional Notation

In a conventional notation used in many studies, a probability space and state space of random variables is identified by its symbol. However, such a notation makes a formula ambiguous in a large equation. This letter proposes to use an index set to identify the probability space and state space of random variables. It is shown that the proposed notation can increase the generality of formulas without ambiguity.

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