The inverse first-passage-place problem for Wiener processes

2021 ◽  
pp. 1-21
Author(s):  
Mario Lefebvre
Keyword(s):  
First Passage ◽  
Wiener Processes

A stochastic ordering of partial sums of independent random variables and of some random processes

1992 ◽  
Vol 29 (03) ◽  
pp. 645-654 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Reliability Theory ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Similar Argument ◽  
First Passage ◽  
Wiener Processes ◽  
Likelihood Ratio Ordering

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 175-184
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a &gt; 0 or −b &lt; 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

A stochastic ordering of partial sums of independent random variables and of some random processes

1992 ◽  
Vol 29 (3) ◽  
pp. 645-654 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Reliability Theory ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Similar Argument ◽  
First Passage ◽  
Wiener Processes ◽  
Likelihood Ratio Ordering

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

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