A note on linear estimation of the intensity in a doubly stochastic Poisson field

1971 ◽  
Vol 8 (03) ◽  
pp. 612-614
Author(s):  
Jan Grandell
Keyword(s):  
Fixed Point ◽  
Linear Estimation ◽  
Linear Estimate ◽  
Borel Set ◽  
Doubly Stochastic ◽  
Intensity Field ◽  
Poisson Field

Summary A realization of a doubly stochastic Poisson field is assumed to be observed in a Borel set S ⊂ Rk. The best linear estimate of the realization of the intensity field (at an arbitrary but fixed point x ∈ S) which generated the observation is obtained.

A note on linear estimation of the intensity in a doubly stochastic Poisson field

1971 ◽  
Vol 8 (3) ◽  
pp. 612-614 ◽  
Author(s):  
Jan Grandell
Keyword(s):  
Fixed Point ◽  
Linear Estimation ◽  
Linear Estimate ◽  
Borel Set ◽  
Doubly Stochastic ◽  
Intensity Field ◽  
Poisson Field

SummaryA realization of a doubly stochastic Poisson field is assumed to be observed in a Borel set S ⊂ Rk. The best linear estimate of the realization of the intensity field (at an arbitrary but fixed point x ∈ S) which generated the observation is obtained.

Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

2020 ◽  
pp. 1-21
Author(s):  
Mostapha Saouli ◽  
B. Mansouri
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Time Interval ◽  
Present Value ◽  
Uniqueness Of Solutions ◽  
Doubly Stochastic ◽  
Teugels Martingales ◽  
The Fixed Point Theorem

We are interested in this paper on reflected anticipated backward doubly stochastic differential equations (RABDSDEs) driven by teugels martingales associated with Levy process. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem where the coefficients of these BDSDEs depend on the future and present value of the solution $\left( Y,Z\right)$. We also show the comparison theorem for a special class of RABDSDEs under some slight stronger conditions. The novelty of our result lies in the fact that we allow the time interval to be infinite.

Mental equilibrium: Identifying fixed-point attractors in the stream of thought

2003 ◽  
Author(s):  
Robin R. Vallacher ◽  
Andrzej Nowak ◽  
Matthew Rockloff
Keyword(s):  
Fixed Point

Bifurcation in a Simple Model of the Cardiovascular System

2000 ◽  
Vol 39 (02) ◽  
pp. 118-121 ◽  
Author(s):  
S. Akselrod ◽  
S. Eyal
Keyword(s):  
Nonlinear Dynamics ◽  
Blood Pressure ◽  
Heart Rate ◽  
Fixed Point ◽  
Cardiovascular System ◽  
Modified Model ◽  
Mayer Waves ◽  
Sustained Oscillations ◽  
Human Cardiovascular System ◽  
Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

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