scholarly journals Mixingale Estimation Function for SPDEs with Random Sampling

2021 ◽  
Vol 2 ◽  
pp. 3
Author(s):  
Jaya P. N. Bishwal
Keyword(s):  
Differential Equation ◽  
Poisson Process ◽  
Random Sampling ◽  
Strong Consistency ◽  
Stochastic Partial Differential Equation ◽  
Estimation Procedure ◽  
Arrival Times ◽  
Estimation Function ◽  
Stage Estimation ◽  
Drift Parameter

We study the mixingale estimation function estimator of the drift parameter in the stochastic partial differential equation when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we substitute this estimate in the estimation function to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the mixingale estimation function estimator.

An Inventory With Constant Demand and Poisson Restocking

1987 ◽  
Vol 1 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Laurence A. Baxter ◽  
Eui Yong Lee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Distribution Function ◽  
Poisson Process ◽  
Stationary Case ◽  
Stieltjes Transform ◽  
Partial Differential

An inventory whose stock decreases linearly with time is considered. The inventory may be replenished at the instants at which a deliveryman arrives provided that the level of the inventory does not exceed a certain threshold; deliveries are made according to a Poisson process. A partial differential equation for the distribution function of the level of the inventory is solved to yield a formula for the corresponding Laplace–Stieltjes transform. The evaluation of the transform is discussed and explicit results are obtained for the stationary case.

Validation of Random Sampling as an Estimation Procedure for Lyme Disease Surveillance in Massachusetts and Minnesota

2016 ◽  
Vol 65 (2) ◽  
pp. 266-274 ◽  
Author(s):  
J. Bjork ◽  
C. Brown ◽  
H. Friedlander ◽  
E. Schiffman ◽  
D. Neitzel
Keyword(s):  
Lyme Disease ◽  
Random Sampling ◽  
Disease Surveillance ◽  
Estimation Procedure

INDIVIDUAL EQUILIBRIUM DYNAMIC ROUTING IN A MULTIPLE SERVER RETRIAL QUEUE

2000 ◽  
Vol 14 (1) ◽  
pp. 9-26 ◽  
Author(s):  
Anthony C. Brooms
Keyword(s):  
Nash Equilibrium ◽  
Poisson Process ◽  
Sojourn Time ◽  
Service System ◽  
Transmission Rate ◽  
Retrial Queue ◽  
Dynamic Learning ◽  
Arrival Times ◽  
The Public ◽  
Expected Sojourn Time

Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate λ. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean μ−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean ν−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

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