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Stochastic Analysis and Applications, 2012
A cost process is associated with a discrete time, finite state Markov chain. Using backward recursion, the distribution of the first time the cost falls below a given level is calculated.
Elliott, R. +2 more
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A cost process is associated with a discrete time, finite state Markov chain. Using backward recursion, the distribution of the first time the cost falls below a given level is calculated.
Elliott, R. +2 more
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2021
This chapter provides methods to assess the probability distribution of a hitting time. It is motivated by applications in predictive reliability in which the probability that a piece of equipment is in operation throughout a given period of time has to be evaluated. It is an opportunity to look at new PDMPs that are obtained from the initial model. We
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This chapter provides methods to assess the probability distribution of a hitting time. It is motivated by applications in predictive reliability in which the probability that a piece of equipment is in operation throughout a given period of time has to be evaluated. It is an opportunity to look at new PDMPs that are obtained from the initial model. We
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The Hitting Time Theorem Revisited
The American Mathematical Monthly, 2011This note presents a very short and simple combinatorial proof of the classical hitting time theorem, or equivalently, the ballot theorem. © The Mathematical Association of America.
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Applied Mathematical Finance, 2004
This paper determines first‐passage time distributions with a twofold emphasis on the dynamics of the state variables and interest rate uncertainty. Underlyings follow two‐dimensional geometric Brownian motions, Ornstein–Uhlenbeck processes or Poisson jump‐diffusion processes, and boundaries are either fixed or indexed on risk‐free bonds.
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This paper determines first‐passage time distributions with a twofold emphasis on the dynamics of the state variables and interest rate uncertainty. Underlyings follow two‐dimensional geometric Brownian motions, Ornstein–Uhlenbeck processes or Poisson jump‐diffusion processes, and boundaries are either fixed or indexed on risk‐free bonds.
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Return-Time Statistics, Hitting-Time Statistics and Inducing
2014In the framework of abstract ergodic probability-preserving transformations, we prove that the limiting return-time statistics and hitting-time statistics persist if we pass from the original system to a first-return map and vice versa.
Zweimüller, Roland +2 more
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First-hitting times under drift
Theoretical Computer Science, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kötzing, Timo (Dr.) +1 more
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1989
In the context of Markov chains, the fundamental use of the heuristic is to estimate the distribution of the first hitting time to a rarely-visited state or set of states. Such problems arise in several areas of applied probability, e.g., queueing theory and reliability, as well as pure theory.
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In the context of Markov chains, the fundamental use of the heuristic is to estimate the distribution of the first hitting time to a rarely-visited state or set of states. Such problems arise in several areas of applied probability, e.g., queueing theory and reliability, as well as pure theory.
openaire +1 more source