scholarly journals Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Caishi Wang ◽  
Jinshu Chen
Keyword(s):  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Convergence Theorems ◽  
Necessary And Sufficient ◽  
Normal Martingale

The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingaleM. A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strongly convergent. A type of generalized martingales associated withMis introduced and their convergence theorems are established. Some applications are also shown.

scholarly journals Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jinshu Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Functional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Convergence Of Operators

We aim to investigate the convergence of operators sequences acting on functionals of discrete-time normal martingales M. We first apply the 2D-Fock transform for operators from the testing functional space S(M) to the generalized functional space S⁎(M) and obtain a necessary and sufficient condition for such operators sequences to be strongly convergent. We then discuss the integration of these operator-valued functions. Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. And also we prove the continuity and continuous dependence on initial values of the solution.

scholarly journals Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
Time Linear

The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.

scholarly journals Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Songlin Wo ◽  
Xiaoxin Han
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient ◽  
Time Linear

The finite-time stability (FTS) problem of discrete-time linear singular systems (DTLSS) is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI) approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

On branching processes allowing immigration

1972 ◽  
Vol 9 (01) ◽  
pp. 24-31 ◽  
Author(s):  
Y. S. Yang
Keyword(s):  
Invariant Measure ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Recurrence ◽  
Discrete Time Case ◽  
Necessary And Sufficient

Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.

scholarly journals Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

The controllability issues for linear discrete-time systems with delay in state are addressed. By introducing a new concept, the minimum controllability realization index (MinCRI), the characteristic of controllability is revealed. It is proved that the MinCRI of a system with state delay exists and is finite. Based on this result, a necessary and sufficient condition for the controllability of discrete-time linear systems with state delay is established.

scholarly journals Weak convergence of conditioned birth-death processes in discrete time

1997 ◽  
Vol 34 (01) ◽  
pp. 46-53
Author(s):  
Pauline Schrijner ◽  
Erik A. Van Doorn
Keyword(s):  
Weak Convergence ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Death Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Absorbing State ◽  
Limiting Behaviour ◽  
Necessary And Sufficient ◽  
Birth Death

We consider a discrete-time birth-death process on the non-negative integers with −1 as an absorbing state and study the limiting behaviour asn →∞ of the process conditioned on non-absorption until timen.By proving that a condition recently proposed by Martinez and Vares is vacuously true, we establish that the conditioned process is always weakly convergent when all self-transition probabilities are zero. In the aperiodic case we obtain a necessary and sufficient condition for weak convergence.

The Galton-Watson predator-prey process

1991 ◽  
Vol 28 (01) ◽  
pp. 9-16 ◽  
Author(s):  
John Coffey ◽  
Wolfgang J. Bühler
Keyword(s):  
Discrete Time ◽  
Sufficient Condition ◽  
Positive Probability ◽  
Necessary And Sufficient Condition ◽  
Predator Prey ◽  
Probability Of Survival ◽  
Predator Prey Model ◽  
Prey Model ◽  
Necessary And Sufficient

A probabilistic predator-prey model is constructed using linked discrete-time branching-type processes. A necessary and sufficient condition for positive probability of survival of both populations is given.

On branching processes allowing immigration

1972 ◽  
Vol 9 (1) ◽  
pp. 24-31 ◽  
Author(s):  
Y. S. Yang
Keyword(s):  
Invariant Measure ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Recurrence ◽  
Discrete Time Case ◽  
Necessary And Sufficient

Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.

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