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Journal articles on the topic 'First Hitting Time'

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Published: 4 June 2021
Last updated: 10 February 2022

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1

Takeuchi, Junji. "First hitting time for Bessel processes." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 8 (1985): 246–48. http://dx.doi.org/10.3792/pjaa.61.246.

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2

Jackson, Ken, Alexander Kreinin, and Wanhe Zhang. "Randomization in the first hitting time problem." Statistics & Probability Letters 79, no. 23 (2009): 2422–28. http://dx.doi.org/10.1016/j.spl.2009.08.016.

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3

Nakajima, Tadashi. "Joint distribution of the first hitting time and first hitting place for a random walk." Kodai Mathematical Journal 21, no. 2 (1998): 192–200. http://dx.doi.org/10.2996/kmj/1138043873.

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4

Cui, Zhenyu, and Duy Nguyen. "First hitting time of integral diffusions and applications." Stochastic Models 33, no. 3 (2017): 376–91. http://dx.doi.org/10.1080/15326349.2017.1300920.

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5

Mazza, Christian. "Asymptotic First Hitting-Time Distribution of Annealing Processes." SIAM Journal on Control and Optimization 32, no. 5 (1994): 1266–88. http://dx.doi.org/10.1137/s0363012991197171.

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6

Yang, Xiangqun, and Shaoyue Liu. "Joint distributions of first hitting time and first hitting location after explosion for birth and death processes." Science in China Series A: Mathematics 43, no. 10 (2000): 1014–18. http://dx.doi.org/10.1007/bf02898234.

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7

Stogiannis, D., C. Caroni, C. E. Anagnostopoulos, and I. K. Toumpoulis. "Comparing first hitting time and proportional hazards regression models." Journal of Applied Statistics 38, no. 7 (2010): 1483–92. http://dx.doi.org/10.1080/02664763.2010.505954.

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8

Maciuca, Romeo, and Song-Chun Zhu. "First Hitting Time Analysis of the Independence Metropolis Sampler." Journal of Theoretical Probability 19, no. 1 (2006): 235–61. http://dx.doi.org/10.1007/s10959-006-0002-9.

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9

Xu, Lin, and Dongjin Zhu. "On the Distribution of First Exit Time for Brownian Motion with Double Linear Time-Dependent Barriers." ISRN Applied Mathematics 2013 (September 26, 2013): 1–5. http://dx.doi.org/10.1155/2013/865347.

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This paper focuses on the first exit time for a Brownian motion with a double linear time-dependent barrier specified by y=a+bt, y=ct, (a>0, b<0, c>0). We are concerned in this paper with the distribution of the Brownian motion hitting the upper barrier before hitting the lower linear barrier. The main method we applied here is the Girsanov transform formula. As a result, we expressed the density of such exit time in terms of a finite series. This result principally provides us an analytical expression for the distribution of the aforementioned exit time and an easy way to compute the
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10

Touboul, Jonathan, and Olivier Faugeras. "A characterization of the first hitting time of double integral processes to curved boundaries." Advances in Applied Probability 40, no. 02 (2008): 501–28. http://dx.doi.org/10.1017/s0001867800002627.

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The problem of finding the probability distribution of the first hitting time of a double integral process (DIP) such as the integrated Wiener process (IWP) has been an important and difficult endeavor in stochastic calculus. It has applications in many fields of physics (first exit time of a particle in a noisy force field) or in biology and neuroscience (spike time distribution of an integrate-and-fire neuron with exponentially decaying synaptic current). The only results available are an approximation of the stationary mean crossing time and the distribution of the first hitting time of the
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11

Touboul, Jonathan, and Olivier Faugeras. "A characterization of the first hitting time of double integral processes to curved boundaries." Advances in Applied Probability 40, no. 2 (2008): 501–28. http://dx.doi.org/10.1239/aap/1214950214.

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The problem of finding the probability distribution of the first hitting time of a double integral process (DIP) such as the integrated Wiener process (IWP) has been an important and difficult endeavor in stochastic calculus. It has applications in many fields of physics (first exit time of a particle in a noisy force field) or in biology and neuroscience (spike time distribution of an integrate-and-fire neuron with exponentially decaying synaptic current). The only results available are an approximation of the stationary mean crossing time and the distribution of the first hitting time of the
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12

Liu, Yuanyuan, and Yanhong Song. "Integral-type functionals of first hitting times for continuous-time Markov chains." Frontiers of Mathematics in China 13, no. 3 (2018): 619–32. http://dx.doi.org/10.1007/s11464-018-0700-5.

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13

de la Peña, Victor, Henryk Gzyl, and Patrick McDonald. "Hitting Time and Inverse Problems for Markov Chains." Journal of Applied Probability 45, no. 3 (2008): 640–49. http://dx.doi.org/10.1239/jap/1222441820.

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Let Wn be a simple Markov chain on the integers. Suppose that Xn is a simple Markov chain on the integers whose transition probabilities coincide with those of Wn off a finite set. We prove that there is an M > 0 such that the Markov chain Wn and the joint distributions of the first hitting time and first hitting place of Xn started at the origin for the sets {-M, M} and {-(M + 1), (M + 1)} algorithmically determine the transition probabilities of Xn.
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14

de la Peña, Victor, Henryk Gzyl, and Patrick McDonald. "Hitting Time and Inverse Problems for Markov Chains." Journal of Applied Probability 45, no. 03 (2008): 640–49. http://dx.doi.org/10.1017/s0021900200004617.

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Let W n be a simple Markov chain on the integers. Suppose that X n is a simple Markov chain on the integers whose transition probabilities coincide with those of W n off a finite set. We prove that there is an M > 0 such that the Markov chain W n and the joint distributions of the first hitting time and first hitting place of X n started at the origin for the sets {-M, M} and {-(M + 1), (M + 1)} algorithmically determine the transition probabilities of X n .
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15

NAKAJIMA, Tadashi, and Sadao SATO. "On the Joint Distribution of the First Hitting Time and the First Hitting Place to the Space-Time Wedge Domain of a Biharmonic Pseudo Process." Tokyo Journal of Mathematics 22, no. 2 (1999): 399–413. http://dx.doi.org/10.3836/tjm/1270041446.

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16

Ross, Sheldon M., and Sridhar Seshadri. "HITTING TIME IN AN ERLANG LOSS SYSTEM." Probability in the Engineering and Informational Sciences 16, no. 2 (2002): 167–84. http://dx.doi.org/10.1017/s0269964802162036.

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In this article, we develop methods for estimating the expected time to the first loss in an Erlang loss system. We are primarily interested in estimating this quantity under light traffic conditions. We propose and compare three simulation techniques as well as two Markov chain approximations. We show that the Markov chain approximations proposed by us are asymptotically exact when the load offered to the system goes to zero. The article also serves to highlight the fact that efficient estimation of transient quantities of stochastic systems often requires the use of techniques that combine a
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17

Abundo, Mario. "The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion." Mathematics 6, no. 6 (2018): 91. http://dx.doi.org/10.3390/math6060091.

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18

Xin Du, Youcong Ni, Ruliang Xiao, and Huang Faliang. "The Expected First Hitting Time of a class of Evolutionary Algorithms." International Journal of Advancements in Computing Technology 3, no. 6 (2011): 160–68. http://dx.doi.org/10.4156/ijact.vol3.issue6.19.

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19

Isozaki, Yasuki. "First hitting time of the integer lattice by symmetric stable processes." Statistics & Probability Letters 98 (March 2015): 50–53. http://dx.doi.org/10.1016/j.spl.2014.12.013.

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20

Isozaki, Yasuki. "The first hitting time of the integers by symmetric Lévy processes." Stochastic Processes and their Applications 129, no. 5 (2019): 1782–94. http://dx.doi.org/10.1016/j.spa.2018.06.001.

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21

Uchiyama, Kohei. "The First Hitting Time of a Single Point for Random Walks." Electronic Journal of Probability 16 (2011): 1960–2000. http://dx.doi.org/10.1214/ejp.v16-931.

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22

Shen, Shih-Yu, and Yi-Long Hsiao. "An Evaluation for the Probability Density of the First Hitting Time." Applied Mathematics 04, no. 05 (2013): 792–96. http://dx.doi.org/10.4236/am.2013.45108.

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23

Lipton, Alexander, and Vadim Kaushansky. "On the first hitting time density for a reducible diffusion process." Quantitative Finance 20, no. 5 (2020): 723–43. http://dx.doi.org/10.1080/14697688.2020.1713394.

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24

Galván-Núñez, Silvia, and Nii Attoh-Okine. "A threshold-regression model for track geometry degradation." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232, no. 10 (2018): 2456–65. http://dx.doi.org/10.1177/0954409718777834.

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Track-related failures are a major factor contributing to train derailments in the United States. Therefore, determining the failure time is critical for safety purposes. Traditionally, failure time in track geometry has been modeled using defect data. However, unless it is an accident due to extreme events, track geometry fails as a result of an underlying degradation process. The first hitting time is referred to the probability distribution of the time at which the degradation path first reaches a safety threshold. This paper presents the formulation and implementation of the first hitting
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25

Hamana, Yuji, Ryo Kaikura, and Kosuke Shinozaki. "Asymptotic expansions for the first hitting times of Bessel processes." Opuscula Mathematica 41, no. 4 (2021): 509–37. http://dx.doi.org/10.7494/opmath.2021.41.4.509.

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26

Hesse, C. H. "Hitting-Time Densities of a Two-Dimensional Markov Process." Probability in the Engineering and Informational Sciences 6, no. 4 (1992): 561–80. http://dx.doi.org/10.1017/s0269964800002734.

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This paper deals with the two-dimensional stochastic process (X(t), V(t)) where dX(t) = V(t)dt, V(t) = W(t) + ν for some constant ν and W(t) is a one-dimensional Wiener process with zero mean and variance parameter σ2= 1. We are interested in the first-passage time of (X(t), V(t)) to the plane X = 0 for a process starting from (X(0) = −x, V(0) = ν) with x > 0. The partial differential equation for the Laplace transform of the first-passage time density is transformed into a Schrödinger-type equation and, using methods of global analysis, such as the method of dominant balance, an approximat
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27

Chia, A., T. Paterek, and L. C. Kwek. "Hitting statistics from quantum jumps." Quantum 1 (July 21, 2017): 19. http://dx.doi.org/10.22331/q-2017-07-21-19.

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We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks in discrete time. This method however, is well-suited to continuous-time problems. It is shown here that a continuous-time hitting problem is amenable to analysis via quantum jumps: The hitting time ca
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28

Kounta, Moussa. "First Passage Time of a Markov Chain That Converges to Bessel Process." Abstract and Applied Analysis 2017 (December 3, 2017): 1–7. http://dx.doi.org/10.1155/2017/7189826.

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We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process.
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29

Abundo, Mario. "On First-Hitting Time of a Linear Boundary by Perturbed Brownian Motion." Open Mathematics Journal 7, no. 1 (2014): 6–8. http://dx.doi.org/10.2174/1874117701407010006.

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30

Lefebvre, Mario. "On the inverse of the first hitting time problem for bidimensional processes." Journal of Applied Probability 34, no. 3 (1997): 610–22. http://dx.doi.org/10.2307/3215088.

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Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinite
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31

Lefebvre, Mario. "On the inverse of the first hitting time problem for bidimensional processes." Journal of Applied Probability 34, no. 03 (1997): 610–22. http://dx.doi.org/10.1017/s0021900200101287.

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Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinite
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32

Hasilová, Kamila, and David Vališ. "Non-parametric estimates of the first hitting time of Li-ion battery." Measurement 113 (January 2018): 82–91. http://dx.doi.org/10.1016/j.measurement.2017.08.030.

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33

Alili, L., P. Patie, and J. L. Pedersen. "Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process1." Stochastic Models 21, no. 4 (2005): 967–80. http://dx.doi.org/10.1080/15326340500294702.

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34

Hishida, Yuji, Yuta Ishigaki, and Toshiki Okumura. "A Numerical Scheme for Expectations with First Hitting Time to Smooth Boundary." Asia-Pacific Financial Markets 26, no. 4 (2019): 553–65. http://dx.doi.org/10.1007/s10690-019-09278-0.

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35

Yushan, Zhang, Huang Han, Hao Zhifeng, and Hu Guiwu. "First hitting time analysis of continuous evolutionary algorithms based on average gain." Cluster Computing 19, no. 3 (2016): 1323–32. http://dx.doi.org/10.1007/s10586-016-0587-4.

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36

Kraft, Holger, and Mogens Steffensen. "Portfolio problems stopping at first hitting time with application to default risk." Mathematical Methods of Operations Research 63, no. 1 (2005): 123–50. http://dx.doi.org/10.1007/s00186-005-0026-4.

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37

Yamamoto, Ken. "Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability." International Journal of Statistical Mechanics 2013 (October 27, 2013): 1–9. http://dx.doi.org/10.1155/2013/831390.

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This paper treats a kind of a one-dimensional first-passage problem, which seeks the probability that a random walker first hits the origin at a specified time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the “halt” that the walker does not hop with a nonzero probability. The solution to the problem is expressed using a Gauss hypergeometric function. The moment generating function of the hitting time is also calculated, and a calculation technique of the moments is developed. The author derives the long-time behavior of the hitting
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38

Jia, Lifen, Waichon Lio, and Wei Chen. "Extreme values, first hitting time and time integral of solution of uncertain spring vibration equation." Journal of Intelligent & Fuzzy Systems 38, no. 3 (2020): 3201–11. http://dx.doi.org/10.3233/jifs-191179.

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39

Sacerdote, Laura, Ottavia Telve, and Cristina Zucca. "Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries." Advances in Applied Probability 46, no. 01 (2014): 186–202. http://dx.doi.org/10.1017/s0001867800006996.

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Consider a one-dimensional diffusion process on the diffusion interval I originated in x 0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t 0, with bounded derivatives, a(t) < b(t), and a(t), b(t) ∈ I, for all t > t 0. We study the joint distribution of the two random variables T a and T b , the first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of T a and T b in terms of ℙ(T a < t, T a < T b ) and ℙ(T b < t, T a > T b ), and we determine a system o
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40

Sacerdote, Laura, Ottavia Telve, and Cristina Zucca. "Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries." Advances in Applied Probability 46, no. 1 (2014): 186–202. http://dx.doi.org/10.1239/aap/1396360109.

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Consider a one-dimensional diffusion process on the diffusion interval I originated in x0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t0, with bounded derivatives, a(t) < b(t), and a(t), b(t) ∈ I, for all t > t0. We study the joint distribution of the two random variables Ta and Tb, the first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of Ta and Tb in terms of ℙ(Ta < t, Ta < Tb) and ℙ(Tb < t, Ta > Tb), and we determine a system of integral equations verified by these last
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41

Whiteside, David, and Machar Reid. "External Match Workloads During the First Week of Australian Open Tennis Competition." International Journal of Sports Physiology and Performance 12, no. 6 (2017): 756–63. http://dx.doi.org/10.1123/ijspp.2016-0259.

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Purpose:With a view to informing athlete preparation leading into tournament play, this study examined external hitting and movement workloads during the first week of the 2012–2016 Australian Open tournaments.Methods:Using Hawk-Eye, on-court movement and stroke data were captured for 39 players (21 women, 18 men) during the first 4 rounds of singles competition. Hitting and movement workloads were compared between sexes and rounds of competition.Results:On average, men traversed approximately 4 km greater distance and hit 785 more shots than women hit across the first 4 rounds of the Australi
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42

Jiang, Jing, Li Dong Meng, and Xiu Mei Xu. "The Study on Convergence and Convergence Rate of Genetic Algorithm Based on an Absorbing Markov Chain." Applied Mechanics and Materials 239-240 (December 2012): 1511–15. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.1511.

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The study on convergence of GA is always one of the most important theoretical issues. This paper analyses the sufficient condition which guarantees the convergence of GA. Via analyzing the convergence rate of GA, the average computational complexity can be implied and the optimization efficiency of GA can be judged. This paper proposes the approach to calculating the first expected hitting time and analyzes the bounds of the first hitting time of concrete GA using the proposed approach.
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43

Chowdhury and, Anirban Narayan, and Rolando D. Somma. "Quantum algorithms for Gibbs sampling and hitting-time estimation." Quantum Information and Computation 17, no. 1&2 (2017): 41–64. http://dx.doi.org/10.26421/qic17.1-2-3.

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We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in p Nβ/Z and polynomial in log(1/epsilon), where N is the Hilbert space dimension, β is the inverse temperature, Z is the partition function, and epsilon is the desired precision of the output state. Our quantum algorithm exponentially improves the complexity dependence on 1/epsilon and polynomially improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates t
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44

Lefebvre, Mario, and Éric Léonard. "On the first hitting place of the integrated Wiener process." Advances in Applied Probability 21, no. 04 (1989): 945–48. http://dx.doi.org/10.1017/s0001867800019182.

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Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).
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45

Lefebvre, Mario, and Éric Léonard. "On the first hitting place of the integrated Wiener process." Advances in Applied Probability 21, no. 4 (1989): 945–48. http://dx.doi.org/10.2307/1427780.

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Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).
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46

Dong, Qinglai, and Lirong Cui. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries." Methodology and Computing in Applied Probability 21, no. 1 (2018): 1–23. http://dx.doi.org/10.1007/s11009-018-9638-z.

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47

Varshney, Neeraj, Werner Haselmayr, and Weisi Guo. "On Flow-Induced Diffusive Mobile Molecular Communication: First Hitting Time and Performance Analysis." IEEE Transactions on Molecular, Biological and Multi-Scale Communications 4, no. 4 (2018): 195–207. http://dx.doi.org/10.1109/tmbmc.2019.2928543.

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48

Stogiannis, D., and C. Caroni. "Issues in Fitting Inverse Gaussian First Hitting Time Regression Models for Lifetime Data." Communications in Statistics - Simulation and Computation 42, no. 9 (2013): 1948–60. http://dx.doi.org/10.1080/03610918.2012.687061.

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49

Yu, Yang, and Zhi-Hua Zhou. "A new approach to estimating the expected first hitting time of evolutionary algorithms." Artificial Intelligence 172, no. 15 (2008): 1809–32. http://dx.doi.org/10.1016/j.artint.2008.07.001.

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50

Locatelli, M. "Convergence and first hitting time of simulated annealing algorithms for continuous global optimization." Mathematical Methods of Operations Research (ZOR) 54, no. 2 (2001): 171–99. http://dx.doi.org/10.1007/s001860100149.

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