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Journal articles on the topic 'First exit time'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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1

Rasova, S. S., and B. P. Harlamov. "Optimal local first exit time." Journal of Mathematical Sciences 159, no. 3 (2009): 327–40. http://dx.doi.org/10.1007/s10958-009-9445-8.

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2

Beccaria, Matteo, Giuseppe Curci, and Andrea Viceré. "Numerical solutions of first-exit-time problems." Physical Review E 48, no. 2 (1993): 1539–46. http://dx.doi.org/10.1103/physreve.48.1539.

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3

Stadje, Wolfgang. "First exit times for integer valued continuous time markov chains." Sequential Analysis 19, no. 3 (2000): 93–114. http://dx.doi.org/10.1080/07474940008836443.

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4

Mselmi, Farouk. "Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator." Filomat 32, no. 7 (2018): 2545–52. http://dx.doi.org/10.2298/fil1807545m.

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This paper deals with a characterization of the first-exit time of the inverse Gaussian subordinator in terms of natural exponential family. This leads us to characterize, by means its variance function, the class of L?vy processes time-changed by the first-exit time of the inverse Gaussian subordinator.

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5

Tugaut, Julian. "Exit-time of mean-field particles system." ESAIM: Probability and Statistics 24 (2020): 399–407. http://dx.doi.org/10.1051/ps/2019028.

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The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain D on ℝd as the diffusion coefficient goes to 0. We establish a Kramers’ type law. In other words, we show that the exit-time is exponentially equivalent to [see formula in PDF], HN being the exit-cost. We also show that this exit-cost converges to some quantity H.

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6

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 distribution of first exit time numerically.

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7

Bal, Guillaume, and Tom Chou. "On the reconstruction of diffusions from first-exit time distributions." Inverse Problems 20, no. 4 (2004): 1053–65. http://dx.doi.org/10.1088/0266-5611/20/4/004.

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8

Zhang, Yong-Chao. "Entry-exit decisions with output reduction during exit periods." AIMS Mathematics 9, no. 3 (2024): 6555–67. http://dx.doi.org/10.3934/math.2024319.

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<abstract><p>In practice, a firm usually reduces the output of a project during exiting the project. We intend to fully analyze the effects of the reduction on the entry-exit decision on the project. To this end, we first obtain the closed expressions of the optimal activating time, optimal start time of the exit, and the maximal expected present value of the project. With these expressions in hand, we completely investigate the effects analytically and numerically. The results show us that the reduction affects the entry-exit decision in different ways due to the different conditions in terms of the parameters involved in the problem. The reduction does not affect the entry-exit decision provided that the firm never exits the project. If the firm exits the project in a finite time, the reduction may postpone or advance the activating time and start time of the exit.</p></abstract>

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9

Stadje, W., and S. Zacks. "UPPER FIRST-EXIT TIMES OF COMPOUND POISSON PROCESSES REVISITED." Probability in the Engineering and Informational Sciences 17, no. 4 (2003): 459–65. http://dx.doi.org/10.1017/s0269964803174025.

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For a compound Poisson process (CPP) with only positive jumps, an elegant formula connects the density of the hitting time for a lower straight line with that of the process itself at time t, h(x; t), considered as a function of time and position jointly. We prove an analogous (albeit more complicated) result for the first time the CPP crosses an upper straight line. We also consider the conditional density of the CPP at time t, given that the upper line has not been reached before t. Finally, it is shown how to compute certain moment integrals of h.

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10

Kim, Yoora, Irem Koprulu та Ness B. Shroff. "First exit time of a Lévy flight from a bounded region in ℝN". Journal of Applied Probability 52, № 3 (2015): 649–64. http://dx.doi.org/10.1239/jap/1445543838.

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In this paper we characterize the mean and the distribution of the first exit time of a Lévy flight from a bounded region inN-dimensional spaces. We characterize tight upper and lower bounds on the tail distribution of the first exit time, and provide the exact asymptotics of the mean first exit time for a given range of step-length distribution parameters.

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11

Kim, Yoora, Irem Koprulu та Ness B. Shroff. "First exit time of a Lévy flight from a bounded region in ℝN". Journal of Applied Probability 52, № 03 (2015): 649–64. http://dx.doi.org/10.1017/s002190020011335x.

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In this paper we characterize the mean and the distribution of the first exit time of a Lévy flight from a bounded region in N-dimensional spaces. We characterize tight upper and lower bounds on the tail distribution of the first exit time, and provide the exact asymptotics of the mean first exit time for a given range of step-length distribution parameters.

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12

Herrmann, Samuel, and Cristina Zucca. "Exact simulation of first exit times for one-dimensional diffusion processes." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 3 (2020): 811–44. http://dx.doi.org/10.1051/m2an/2019077.

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The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability… The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.

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13

Ozel, Gamze. "On The Mean First Exit Time For A Compound Poisson Process." Journal of Data Science 14, no. 2 (2021): 347–64. http://dx.doi.org/10.6339/jds.201604_14(2).0007.

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14

Harlamov, B. P. "Stochastic integral in the case of infinite expected first exit time." Journal of Mathematical Sciences 147, no. 4 (2007): 6962–74. http://dx.doi.org/10.1007/s10958-007-0522-6.

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15

Patie, P., and C. Winter. "First exit time probability for multidimensional diffusions: A PDE-based approach." Journal of Computational and Applied Mathematics 222, no. 1 (2008): 42–53. http://dx.doi.org/10.1016/j.cam.2007.10.043.

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16

Alzubaidi, Hasan, and Tony Shardlow. "Improved Simulation Techniques for First Exit Time of Neural Diffusion Models." Communications in Statistics - Simulation and Computation 43, no. 10 (2014): 2508–20. http://dx.doi.org/10.1080/03610918.2012.755197.

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17

Adler, J., A. Aharony, and D. Stauffer. "First exit time of termites and random super-normal conductor networks." Journal of Physics A: Mathematical and General 18, no. 3 (1985): L129—L136. http://dx.doi.org/10.1088/0305-4470/18/3/006.

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18

Hurtado, A., S. Markvorsen, and V. Palmer. "Estimates of the first Dirichlet eigenvalue from exit time moment spectra." Mathematische Annalen 365, no. 3-4 (2015): 1603–32. http://dx.doi.org/10.1007/s00208-015-1316-7.

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19

REN, DAN. "OPTIMAL STOPPING FOR THE LAST EXIT TIME." Bulletin of the Australian Mathematical Society 99, no. 1 (2018): 148–60. http://dx.doi.org/10.1017/s0004972718000990.

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Given a one-dimensional downwards transient diffusion process $X$, we consider a random time $\unicode[STIX]{x1D70C}$, the last exit time when $X$ exits a certain level $\ell$, and detect the optimal stopping time for it. In particular, for this random time $\unicode[STIX]{x1D70C}$, we solve the optimisation problem $\inf _{\unicode[STIX]{x1D70F}}\mathbb{E}[\unicode[STIX]{x1D706}(\unicode[STIX]{x1D70F}-\unicode[STIX]{x1D70C})_{+}+(1-\unicode[STIX]{x1D706})(\unicode[STIX]{x1D70C}-\unicode[STIX]{x1D70F})_{+}]$ over all stopping times $\unicode[STIX]{x1D70F}$. We show that the process should stop optimally when it runs below some fixed level $\unicode[STIX]{x1D705}_{\ell }$ for the first time, where $\unicode[STIX]{x1D705}_{\ell }$ is the unique solution in the interval $(0,\unicode[STIX]{x1D706}\ell )$ of an explicitly defined equation.

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20

Schultz, Paul, Frank Hellmann, Kevin N. Webster, and Jürgen Kurths. "Bounding the first exit from the basin: Independence times and finite-time basin stability." Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 4 (2018): 043102. http://dx.doi.org/10.1063/1.5013127.

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21

Zhang, Hui Zeng, Min Zhi Zhao, and Lei Wang. "On first returning time and last exit time of a class of Markov chain." Acta Mathematica Sinica, English Series 29, no. 2 (2012): 331–44. http://dx.doi.org/10.1007/s10114-012-1019-x.

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22

Geiss, Christel, Antti Luoto, and Paavo Salminen. "On first exit times and their means for Brownian bridges." Journal of Applied Probability 56, no. 3 (2019): 701–22. http://dx.doi.org/10.1017/jpr.2019.42.

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AbstractFor a Brownian bridge from 0 to y, we prove that the mean of the first exit time from the interval $\left( -h,h \right),h>0$ , behaves as ${\mathrm{O}}(h^2)$ when $h \downarrow 0$ . Similar behaviour is also seen to hold for the three-dimensional Bessel bridge. For the Brownian bridge and three-dimensional Bessel bridge, this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to provide a detailed proof of an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.

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23

Aurzada, Frank, Frank Aurzada, Михаил Анатольевич Лифшиц, and Mikhail Anatolievich Lifshits. "The first exit time of fractional Brownian motion from a parabolic domain." Teoriya Veroyatnostei i ee Primeneniya 64, no. 3 (2019): 610–20. http://dx.doi.org/10.4213/tvp5262.

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Изучается момент первого выхода многомерного дробного броуновского движения из неограниченных областей. В частности, исследуется верхний хвост соответствующего распределения в случае, когда область имеет форму параболы.

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24

Hosseini, Majid. "On the Conditional Expectation of the First Exit Time of Brownian Motion." Rocky Mountain Journal of Mathematics 39, no. 2 (2009): 563–72. http://dx.doi.org/10.1216/rmj-2009-39-2-563.

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25

Zhou, Yinbing, and Dawei Lu. "The first exit time of fractional Brownian motion from an unbounded domain." Statistics & Probability Letters 218 (March 2025): 110319. https://doi.org/10.1016/j.spl.2024.110319.

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26

Aurzada, F., and M. A. Lifshits. "The First Exit Time of Fractional Brownian Motion from a Parabolic Domain." Theory of Probability & Its Applications 64, no. 3 (2019): 490–97. http://dx.doi.org/10.1137/s0040585x97t989659.

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27

Borodin, A. N. "On the first exit time from an interval for diffusions with jumps." Journal of Mathematical Sciences 163, no. 4 (2009): 352–62. http://dx.doi.org/10.1007/s10958-009-9678-6.

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28

D’Onofrio, G., and E. Pirozzi. "Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes." Methodology and Computing in Applied Probability 21, no. 3 (2018): 735–52. http://dx.doi.org/10.1007/s11009-018-9617-4.

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29

Chiu, Sung Nok, and Chuan Cun Yin. "The first exit time and ruin time for a risk process with reserve-dependent income." Statistics & Probability Letters 60, no. 4 (2002): 417–24. http://dx.doi.org/10.1016/s0167-7152(02)00311-5.

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30

Zhang, Hongxia, Wei Xu, Qin Guo, Ping Han, and Yan Qiao. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise." Chaos, Solitons & Fractals 135 (June 2020): 109767. http://dx.doi.org/10.1016/j.chaos.2020.109767.

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31

Lefebvre, Mario, and Romain Mrad. "First Exit and Optimization Problems for a CIR Diffusion Process." WSEAS TRANSACTIONS ON MATHEMATICS 24 (May 23, 2025): 382–88. https://doi.org/10.37394/23206.2025.24.36.

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Let {X(t), t ≥ 0} be a CIR diffusion process, and τ (x) be the first time that X(t) = 0 or c, given that X(0) = x ∈ (0, c). First, we compute the moment-generating function and the expected value of τ (x). Then, an optimal control problem is considered for {X(t), t ≥ 0}. Finally, we add jumps to the diffusion process and we calculate in a particular case the probability that X(τ (x)) = 0, as well as the expected time needed to leave the interval (0, c). Explicit and exact results are obtained.

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32

Skiadas, Christos H., and Charilaos Skiadas. "The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System." Methodology and Computing in Applied Probability 22, no. 4 (2019): 1601–11. http://dx.doi.org/10.1007/s11009-019-09699-4.

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33

Di Crescenzo, Antonio, Virginia Giorno, Amelia G. Nobile, and Serena Spina. "First-exit-time problems for two-dimensional Wiener and Ornstein–Uhlenbeck processes through time-varying ellipses." Stochastics 96, no. 1 (2024): 696–727. http://dx.doi.org/10.1080/17442508.2024.2315274.

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34

Stadje, W., and S. Zacks. "ON THE UPPER FIRST-EXIT TIMES OF COMPOUND G/M PROCESSES." Probability in the Engineering and Informational Sciences 19, no. 3 (2005): 397–403. http://dx.doi.org/10.1017/s0269964805050230.

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For a compound process with exponential jumps at renewal times, we determine, in closed form, the density of the first time an upper linear boundary is crossed. It is shown how simple formulas for the Laplace transform and the first two moments can be directly derived from this density.

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35

Bañuelos, R., and B. Øksendal. "Exit times for elliptic diffusions and BMO." Proceedings of the Edinburgh Mathematical Society 30, no. 2 (1987): 273–87. http://dx.doi.org/10.1017/s0013091500028339.

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In 1948 P. Lévy formulated the following theorem: If U is an open subset of the complex plane and f:U → ℂ is a nonconstant analytic function, then f maps a 2-dimensional Brownian motion Bt (up to the exit time from U) into a time changed 2-dimensional Brownian motion. A rigorous proof of this result first appeared in McKean [22]. This theorem has been used by many authors to solve problems about analytic functions by reducing them to problems about Brownian motion where the arguments are often more transparent. The survey paper [8] is a good reference for some of these applications. Lévy's theorem has been generalized, first by Bernard, Campbell, and Davie [5], and subsequently by Csink and Øksendal [7]. In Section 1 of this note we use these generalizations of Lévy's theorem to extend some results about BMO functions in the unit disc to harmonic morphisms in ℝn to holomorphic functions in ℂn and to analytic functions on Riemann surfaces. In Section 2, we characterize the domains in ℝn which have the property that the expected exit time of elliptic diffusions is uniformly bounded as a function of the starting point. This extends a result of Hayman and Pommerenke [15], and Stegenga [24] about BMO domains in the complex plane.

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36

Skiadas, Charilaos, and Christos H. Skiadas. "Development, Simulation, and Application of First-Exit-Time Densities to Life Table Data." Communications in Statistics - Theory and Methods 39, no. 3 (2010): 444–51. http://dx.doi.org/10.1080/03610920903140023.

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37

Li, Wenbo V. "The first exit time of a Brownian motion from an unbounded convex domain." Annals of Probability 31, no. 2 (2003): 1078–96. http://dx.doi.org/10.1214/aop/1048516546.

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38

陈, 慧琴. "A Computational Analysis for First Mean Exit Time under Symmetrical Levy Multiplicative Noise." Advances in Applied Mathematics 02, no. 04 (2013): 141–46. http://dx.doi.org/10.12677/aam.2013.24018.

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39

Acharyya, Muktish. "Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour." Applied Mathematics 07, no. 12 (2016): 1353–58. http://dx.doi.org/10.4236/am.2016.712119.

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40

Peng, Qidi, and Nan Rao. "Fractional Brownian motion: Small increments and first exit time from one-sided barrier." Chaos, Solitons & Fractals 177 (December 2023): 114218. http://dx.doi.org/10.1016/j.chaos.2023.114218.

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41

Peng, Jun, and Zaiming Liu. "First Passage Time Moments of Jump-Diffusions with Markovian Switching." International Journal of Stochastic Analysis 2011 (March 20, 2011): 1–11. http://dx.doi.org/10.1155/2011/501360.

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Using an integral equation associated with generalized backward Kolmogorov's equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of jump-diffusions with Markovian switching. The results are used to find the expectation of first passage time of some financial models.

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42

Hu, Jun, Zhongwen Li, Lei You, Hong Zhang, Juan Wei, and Mei Li. "Simulation of queuing time in crowd evacuation by discrete time loss queuing method." International Journal of Modern Physics C 30, no. 08 (2019): 1950057. http://dx.doi.org/10.1142/s0129183119500578.

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We have proposed a new evacuation model based on discrete time loss queuing method in order to effectively depict the queuing of pedestrians in an indoor space and its effect over evacuation performance. In this model, the calculation formula of pedestrian movement probability is given first based on field value and average queuing time; the average queuing time is depicted with the discrete time loss queuing method and the adopted evacuation strategy is set forth through defining cellular evolution process. Moreover, with the use of the established simulation platform for experiment, we have made a deep study of relations of parameters such as evacuation time, pedestrian density, exit number and average queuing time to obtain the pedestrian flow characteristic more in line with the reality. The result has shown that there is a great change in the evacuated population in the change of crowded state at the exit, and in the background of high population density, it is beneficial for reducing queuing time to prefer faraway exit to overcrowded exit for evacuation.

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43

Li, Peng, Chuancun Yin, and Ming Zhou. "The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/675202.

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We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.

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44

Hu, Xiangmin, Tao Chen, Jianyu Wang, Xiang Liu, Meng Li, and Zhanhui Sun. "Characteristics of pedestrian evacuation from narrow seated area considering exit failure: experimental and simulation results." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 3 (2024): 033401. http://dx.doi.org/10.1088/1742-5468/ad2b59.

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Abstract Narrow seated spaces with multiple exits are prevalent structures in public buildings, underscoring the paramount importance of facilitating swift evacuation in such constrained environments. In this study, we first conducted evacuation experiments in a realistic narrow seated area. By manipulating different availability conditions for two exits located at the ends of the long aisle, we studied the effects of unpredictable exit failures, specifically, how the exit switch and explicit guidance influence the evacuation process. The movement characteristics are explored in several aspects, such as pre-evacuation time, aisle conflicts, speed, distance headway, evacuation time, and time lapse. We found that once people have encountered the exit failure condition, they would demonstrate enhanced preparedness in subsequent trials, leading to expedited exit switches. With explicit guidance, people would be less hesitant and move faster in the main aisle. The fine-grid cellular automata model is extended based on the experimental observations to verify its feasibility in simulating this process. Conflict resolution and turning behavior are incorporated for a more nuanced description. The effects of the exit switch are parameterized through the informed probability and the speed reduction.

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45

Gatto, Riccardo. "The von Mises–Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time." Statistics & Probability Letters 83, no. 7 (2013): 1669–76. http://dx.doi.org/10.1016/j.spl.2013.03.010.

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46

Zhou, Xiaowen. "Some fluctuation identities for Lévy processes with jumps of the same sign." Journal of Applied Probability 41, no. 4 (2004): 1191–98. http://dx.doi.org/10.1239/jap/1101840564.

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We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

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47

Zhou, Xiaowen. "Some fluctuation identities for Lévy processes with jumps of the same sign." Journal of Applied Probability 41, no. 04 (2004): 1191–98. http://dx.doi.org/10.1017/s0021900200020957.

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We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

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48

BEVERIDGE, ANDREW. "A Hitting Time Formula for the Discrete Green's Function." Combinatorics, Probability and Computing 25, no. 3 (2015): 362–79. http://dx.doi.org/10.1017/s0963548315000152.

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The discrete Green's function (without boundary)$\mathbb{G}$is a pseudo-inverse of the combinatorial Laplace operator of a graphG= (V, E). We reveal the intimate connection between Green's function and the theory of exact stopping rules for random walks on graphs. We give an elementary formula for Green's function in terms of state-to-state hitting times of the underlying graph. Namely,$\mathbb{G}(i,j) = \pi_j \bigl( H(\pi,j) - H(i,j) \bigr),$where πiis the stationary distribution at vertexi,H(i, j) is the expected hitting time for a random walk starting from vertexito first reach vertexj, andH(π,j) = ∑k∈VπkH(k, j). This formula also holds for the digraph Laplace operator.The most important characteristics of a stopping rule are its exit frequencies, which are the expected number of exits of a given vertex before the rule halts the walk. We show that Green's function is, in fact, a matrix of exit frequencies plus a rank one matrix. In the undirected case, we derive spectral formulas for Green's function and for some mixing measures arising from stopping rules. Finally, we further explore the exit frequency matrix point of view, and discuss a natural generalization of Green's function for any distribution τ defined on the vertex set of the graph.

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49

Bañuelos, Rodrigo, R. Dante DeBlassie, and Robert Smits. "The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola." Annals of Probability 29, no. 2 (2001): 882–901. http://dx.doi.org/10.1214/aop/1008956696.

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50

DeBlassie, R. Dante. "The First Exit Time of a Two-Dimensional Symmetric Stable Process from a Wedge." Annals of Probability 18, no. 3 (1990): 1034–70. http://dx.doi.org/10.1214/aop/1176990735.

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