A martingale approach to first passage problems and a new condition for Wald's identity

2005 ◽  
pp. 146-156 ◽  
Author(s):  
A. A. Novikov
Keyword(s):  
First Passage ◽  
Martingale Approach ◽  
Wald's Identity

An alternative to Wiener-Hopf methods for the study of bounded processes

1964 ◽  
Vol 1 (01) ◽  
pp. 85-120 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Waiting Time ◽  
Finite Interval ◽  
Time Process ◽  
First Passage ◽  
Discrete Parameter ◽  
Waiting Time Process ◽  
Image Position ◽  
Wald's Identity ◽  
Independent Identically Distributed ◽  
The Continuum

Homogeneous additive processes on a finite or semi-infinite interval have been studied in many forms. Wald's identity for the first passage process on the finite interval (see for example Miller, 1961), the waiting time process of Lindley (1952), and a variety of problems in the theory of queues, dams, and inventories come to mind. These processes have been treated by and large by methods in the complex plane. Lindley's discrete parameter process on the continuum, for example, described by where the ξ n are independent identically distributed random variables, has been discussed by Wiener-Hopf methods in recent years by Lindley (1952), Smith (1953), Kemperman (1961), Keilson (1961), and many others. A review of earlier studies is given by Kemperman.

An alternative to Wiener-Hopf methods for the study of bounded processes

1964 ◽  
Vol 1 (1) ◽  
pp. 85-120 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Waiting Time ◽  
Finite Interval ◽  
Time Process ◽  
First Passage ◽  
Discrete Parameter ◽  
Waiting Time Process ◽  
Image Position ◽  
Wald's Identity ◽  
Independent Identically Distributed ◽  
The Continuum

Homogeneous additive processes on a finite or semi-infinite interval have been studied in many forms. Wald's identity for the first passage process on the finite interval (see for example Miller, 1961), the waiting time process of Lindley (1952), and a variety of problems in the theory of queues, dams, and inventories come to mind. These processes have been treated by and large by methods in the complex plane. Lindley's discrete parameter process on the continuum, for example, described by where the ξn are independent identically distributed random variables, has been discussed by Wiener-Hopf methods in recent years by Lindley (1952), Smith (1953), Kemperman (1961), Keilson (1961), and many others. A review of earlier studies is given by Kemperman.

scholarly journals Martingale Approach to Derive Lundberg-Type Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1742
Author(s):  
Tautvydas Kuras ◽  
Jonas Sprindys ◽  
Jonas Šiaulys
Keyword(s):  
Upper Bound ◽  
Ruin Probability ◽  
Risk Model ◽  
Tail Probability ◽  
Martingale Approach ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Wald's Identity

In this paper, we find the upper bound for the tail probability Psupn⩾0∑I=1nξI>x with random summands ξ1,ξ2,… having light-tailed distributions. We find conditions under which the tail probability of supremum of sums can be estimated by quantity ϱ1exp{−ϱ2x} with some positive constants ϱ1 and ϱ2. For the proof we use the martingale approach together with the fundamental Wald’s identity. As the application we derive a few Lundberg-type inequalities for the ultimate ruin probability of the inhomogeneous renewal risk model.

Monitoring of pancreatic graft perfusion by first passage radionuclide angiography

1988 ◽  
Vol 29 (1) ◽  
pp. 138-140
Author(s):  
H. S. Thomsen ◽  
K. Rasmussen ◽  
F. Burcharth ◽  
S. L. Nielsen
Keyword(s):  
Radionuclide Angiography ◽  
First Passage ◽  
Pancreatic Graft

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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