Journal ArticleDOI
Fluctuation Problems for Bernoulli Trials
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In this paper, a simple explicit formula is given for the distribution of the number of changes of luck in n Bernoulli trials with probability $p(0 < p < 1)$ for success.Abstract:
In this paper a simple explicit formula is given for the distribution of the number of changes of luck in n Bernoulli trials with probability $p(0 < p < 1)$ for success.read more
Citations
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Journal ArticleDOI
Limit distributions for the Bernoulli meander
TL;DR: In this paper, the authors studied the limit behavior of the distributions and the moments of the Bernoulli meander in the case where the number of steps in the random walk tends to infinity.
Journal ArticleDOI
On a generalization of the arc-sine law
TL;DR: In this paper, it was shown that the distribution function of the sojourn time of Brownian motion with drift can be expressed simply as a single integral, which is a generalization of the arc-sine law of Paul Levy.
Journal ArticleDOI
On the Local Time of the Brownian Motion
TL;DR: In this paper, explicit formulas for the distribution function, the density function and the moments of the local time of the reflecting Brownian motion process are given for the reflecting motion process.
Book ChapterDOI
On the Local Time of the Brownian Bridge
TL;DR: The notion of local time at level α was introduced by P. Levy as discussed by the authors, where τ(α) is a nonnegative random variable that is called the local time, and α is the normal distribution function.
References
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Journal ArticleDOI
On the Classical Ruin Problems
TL;DR: In this article, simple and elementary proofs are given for the various formulas for Pn (a,b) and it is shown how these formulas can be applied in the theories of order statistics, random walks, storage, queues, and dams.
Journal ArticleDOI
A two-dimensional operator identity with application to the change of sign in sums of random variables
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