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186,615
Randomization in the First Hitting Time Problem ∗
, 2009
"... In this paper we consider the following inverse problem for the first hitting time distribution: given a Wiener process with a random initial state, probability distribution, F(t), and a linear boundary, b(t) = µt, find a distribution of the initial state such that the distribution of the first hit ..."
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In this paper we consider the following inverse problem for the first hitting time distribution: given a Wiener process with a random initial state, probability distribution, F(t), and a linear boundary, b(t) = µt, find a distribution of the initial state such that the distribution of the first
of the first hitting times of Bessel processes ∗
"... Asymptotics of the probability distributions ..."
THE PROBABILITY DISTRIBUTIONS OF THE FIRST HITTING TIMES OF BESSEL PROCESSES
"... Abstract. We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions by means of the zeros of the Bessel functions. The resulting formula is simpler and easier to treat than the corresponding results which have already been obtained. 1. ..."
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Cited by 14 (1 self)
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Abstract. We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions by means of the zeros of the Bessel functions. The resulting formula is simpler and easier to treat than the corresponding results which have already been obtained. 1.
A New Approach to Estimating the Expected First Hitting Time of Evolutionary Algorithms
"... The expected first hitting time is an important issue in theoretical analyses of evolutionary algorithms since it implies the average computational time complexity. In this paper, by exploiting the relationship between the convergence rate and the expected first hitting time, a new approach to estim ..."
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The expected first hitting time is an important issue in theoretical analyses of evolutionary algorithms since it implies the average computational time complexity. In this paper, by exploiting the relationship between the convergence rate and the expected first hitting time, a new approach
Representations of the first hitting time density of an OrnsteinUhlenbeck process
- Stoch. Models
"... Three expressions are provided for the first hitting time density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the parabolic cylinder functions. The second is an integral representation involving some special functions wherea ..."
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Cited by 32 (1 self)
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Three expressions are provided for the first hitting time density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the parabolic cylinder functions. The second is an integral representation involving some special functions
On the expectation of normalized Brownian functionals up to first hitting times
, 2013
"... Let B be a Brownian motion and T1 its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of BUT1 / √ T1, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered. ..."
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Cited by 3 (3 self)
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Let B be a Brownian motion and T1 its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of BUT1 / √ T1, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.
Convergence and First Hitting Time of Simulated Annealing Algorithms for Continuous Global Optimization
"... In this paper simulated annealing algorithms for continuous global optimization are considered. Under the simplifying assumption of known optimal value, the convergence of the algorithms and an upper bound for the expected first hitting time, i.e. the expected number of iterations before reaching th ..."
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Cited by 6 (1 self)
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In this paper simulated annealing algorithms for continuous global optimization are considered. Under the simplifying assumption of known optimal value, the convergence of the algorithms and an upper bound for the expected first hitting time, i.e. the expected number of iterations before reaching
First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
, 2008
"... We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W-i ..."
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Cited by 2 (1 self)
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We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W
Finite first hitting time versus stochastic convergence in particle swarm optimisation
- Proc. of the 9th Metaheuristics International Conference (MIC 2011
"... We reconsider stochastic convergence analyses of particle swarm op-timisation, and point out that previously obtained parameter conditions are not always sufficient to guarantee mean square convergence to a lo-cal optimum. We show that stagnation can in fact occur for non-trivial configurations in n ..."
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Cited by 2 (0 self)
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of algorithms, we suggest the expected first hitting time (FHT), i. e., the time until a search point in the vicinity of the optimum is visited. It is shown that a basic PSO may have infinite expected FHT, while an algorithm introduced here, the Noisy PSO, has finite expected FHT on some functions. 1
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