A note on the gambling team method [PDF]
, 2013 Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated ...
Zajkowski, Krzysztof
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Further studies on square-root boundaries for Bessel processes [PDF]
, 2018 We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries.
Alili, Larbi, Matsumoto, Hiroyuki
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Exponential moments of first passage times and related quantities for random walks [PDF]
, 2010 For a zero-delayed random walk on the real line, let $\tau(x)$, $N(x)$ and $\rho(x)$ denote the first passage time into the interval $(x,\infty)$, the number of visits to the interval $(-\infty,x]$ and the last exit time from $(-\infty,x]$, respectively.
Iksanov, Alexander, Meiners, Matthias
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A note on exponentially bounded stopping times of certain one‐sample sequential rank order tests
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 3, Page 549-554, 1985., 1985 A simple proof of the exponential boundedness of the stopping time of the one‐sample sequential probability ratio tests (SPRT′s) is obtained.
Z. Govindarajulu
wiley +1 more source
A Proof of the Bomber Problem's Spend-It-All Conjecture [PDF]
, 2010 The Bomber Problem concerns optimal sequential allocation of partially effective ammunition $x$ while under attack from enemies arriving according to a Poisson process over a time interval of length $t$.
Bartroff, Jay
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On approximation rates for boundary crossing probabilities for the multivariate Brownian motion process [PDF]
, 2015 Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary.
Borovkov, K., McKinlay, S.
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A random walk version of Robbins' problem: small horizon [PDF]
, 2018 In Robbins' problem of minimizing the expected rank, a finite sequence of $n$ independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected variable ...
Allaart, Pieter C., Allen, Andrew
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Estimation of Gini Index within Pre-Specied Error Bound [PDF]
, 2015 Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width.
Chattopadhyay, Bhargab +1 more
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Stopping times are hitting times: a natural representation
, 2012 There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c\`agl\`ad (LCRL) processes that are non-increasing and take the values 0 and 1 only.
Bass +6 more
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Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations
, 2005 Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, i=1,2,....
Kosters, Holger
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