共查询到20条相似文献,搜索用时 31 毫秒
1.
Robert C. Dalang T. Mountford 《Transactions of the American Mathematical Society》2003,355(3):967-985
A classical and important property of Brownian motion is that given its zero set, distinct excursions away from zero are independent. In this paper, we examine the analogous question for the Brownian sheet, and also for additive Brownian motion. Our main result is that given the level set of the Brownian sheet at level zero, distinct excursions of the sheet away from zero are not independent. In fact, given the zero set of the Brownian sheet in the entire non-negative quadrant, and the sign of all but a finite number of excursions away from zero, the signs of the remaining excursions are determined. For additive Brownian motion, we prove the following definitive result: given the zero set of additive Brownian motion and the sign of a single excursion, the signs of all other excursions are determined. In an appendix by John B. Walsh, it is shown that given the absolute value of the sheet in the entire quadrant and, in addition, the sign of the sheet at a fixed, non-random time point, then the whole sheet can be recovered.
2.
Let T be a plane rooted tree with n nodes which is regarded as family tree of a Galton-Watson branching process conditioned on the total progeny. The profile of the tree may be described by the number of nodes or the number of leaves in layer , respectively. It is shown that these two processes converge weakly to Brownian excursion local time. This is done via characteristic functions obtained by means of generating functions arising from the combinatorial setup and complex contour integration. Besides, an integral representation for the two-dimensional density of Brownian excursion local time is derived. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10 , 421–451, 1997 相似文献
3.
The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula. 相似文献
4.
Brownian sheet images and Bessel-Riesz capacity 总被引:3,自引:0,他引:3
Davar Khoshnevisan 《Transactions of the American Mathematical Society》1999,351(7):2607-2622
We show that the image of a 2-dimensional set under -dimensional, 2-parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive ()-dimensional Bessel-Riesz capacity. Our methods solve a problem of J.-P. Kahane.
5.
Pitman and Yor(20, 21) recently studied the distributions related to the ranked excursion heights of a Brownian bridge. In this paper, we study the asymptotic properties of the ranked heights of Brownian excursions. The heights of both high and low excursions are characterized by several integral tests and laws of the iterated logarithm. Our analysis relies on the distributions of the ranked excursion heights considered up to some random times. 相似文献
6.
Davar Khoshnevisan Zhan Shi 《Transactions of the American Mathematical Society》1998,350(10):4253-4264
The small ball problem for the integrated process of a real-valued Brownian motion is solved. In sharp contrast to more standard methods, our approach relies on the sample path properties of Brownian motion together with facts about local times and Lévy processes.
7.
Christopher Hoffman Douglas Rizzolo Erik Slivken 《Random Structures and Algorithms》2017,50(3):394-419
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017 相似文献
8.
N. Demni 《Journal of Theoretical Probability》2008,21(1):118-143
In this paper, we define and study two parameters dependent free processes (λ,θ) called free Jacobi, obtained as the limit of its matrix counterpart when the size of the matrix goes to infinity. The main result we derive
is a free SDE analogous to that satisfied in the matrix setting, derived under injectivity assumptions. Once we did, we examine
a particular case for which the spectral measure is explicit and does not depend on time (stationary). This allows us to determine
easily the parameters range ensuring our injectivity requirements so that our result applies. Then, we show that under an
additional condition of invertibility at time t=0, this range extends to the general setting. To proceed, we set a recurrence formula for the moments of the process via
free stochastic calculus. 相似文献
9.
L. Chaumont 《Journal of Theoretical Probability》2000,13(1):259-277
Vervaat(18) proved that by exchanging the pre-minimum and post-minimum parts of a Brownian bridge one obtains a normalized Brownian excursion. Let s (0, 1), then we extend this result by determining a random time m
s such that when we exchange the pre-m
s-part and the post-m
s-part of a Brownian bridge, one gets a Brownian bridge conditioned to spend a time equal to s under 0. This transformation leads to some independence relations between some functionals of the Brownian bridge and the time it spends under 0. By splitting the Brownian motion at time m
s in another manner, we get a new path transformation which explains an identity in law on quantiles due to Port. It also yields a pathwise construction of a Brownian bridge conditioned to spend a time equal to s under 0. 相似文献
10.
Reinhard Lang 《Mathematische Nachrichten》1998,193(1):75-91
We consider reflecting Brownian motion in a bounded domain with smooth boundary. Formulas for the moments of the excursion lengths are derived and connections between excursion theory of reflecting Brownian motion and notions from recurrent potential theory are explored. 相似文献
11.
Masatoshi Fukushima Jiangang Ying 《Proceedings of the American Mathematical Society》2003,131(5):1607-1610
In this short article we shall consider the Dirichlet space associated with the distorted Brownian motion on a one-dimensional closed interval and prove that it admits no proper regular Dirichlet subspaces.
12.
A ``lip domain' is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction attains its maximum and minimum at the boundary points at the extreme left and right. This settles the ``hot spots' conjecture for lip domains as well as two conjectures of Jerison and Nadirashvili. Our techniques are probabilistic in nature and may have independent interest.
13.
Gregory F. Lawler José A. Trujillo Ferreras 《Transactions of the American Mathematical Society》2007,359(2):767-787
The Brownian loop soup introduced by Lawler and Werner (2004) is a Poissonian realization from a -finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Komlós, Major, and Tusnády. To make the paper self-contained, we include a proof of the approximation result that we need.
14.
Biao Zhang 《Transactions of the American Mathematical Society》1996,348(1):173-185
We extend some bounds on the variance of the lifetime of two--dimensional Brownian motion, conditioned to exit a planar domain at a given point, to certain domains in higher dimensions. We also give a short ``analytic' proof of some existing results.
15.
Mikló s Csö rgo Lajos Horvá th Piotr Kokoszka 《Proceedings of the American Mathematical Society》2000,128(8):2457-2464
We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.
16.
Stefano Bonaccorsi Lorenzo Zambotti 《Proceedings of the American Mathematical Society》2004,132(3):875-883
We prove infinite-dimensional integration by parts formulae for the laws of the Brownian Meander, of the Bessel Bridge of dimension 3 between and of the Brownian Motion on the set of all paths taking values greater than or equal to a nonpositive constant. We give applications to SPDEs with reflection.
17.
《Stochastic Processes and their Applications》2001,95(1):151-176
Motivated by questions related to a fragmentation process which has been studied by Aldous, Pitman, and Bertoin, we use the continuous-time ballot theorem to establish some results regarding the lengths of the excursions of Brownian motion and related processes. We show that the distribution of the lengths of the excursions below the maximum for Brownian motion conditioned to first hit λ>0 at time t is not affected by conditioning the Brownian motion to stay below a line segment from (0,c) to (t,λ). We extend a result of Bertoin by showing that the length of the first excursion below the maximum for a negative Brownian excursion plus drift is a size-biased pick from all of the excursion lengths, and we describe the law of a negative Brownian excursion plus drift after this first excursion. We then use the same methods to prove similar results for the excursions of more general Markov processes. 相似文献
18.
M. Manickam B. Ramakrishnan 《Transactions of the American Mathematical Society》2000,352(6):2601-2617
In this paper, we set up Shimura and Shintani correspondences between Jacobi forms and modular forms of integral weight for arbitrary level and character, and generalize the Eichler-Zagier isomorphism between Jacobi forms and modular forms of half-integral weight to higher levels. Using this together with the known results, we get a strong multiplicity 1 theorem in certain cases for both Jacobi cusp newforms and half-integral weight cusp newforms. As a consequence, we get, among other results, the explicit Waldspurger theorem.
19.
EXCURSIONS AND LEVY SYSTEM OF BOUNDARY PROCESS*** 总被引:2,自引:2,他引:0
In this paper, the authors investigate the joint distribution of end points of excursion awayfrom a closed set straddling on a fixed time and use this result to compute the Levy systemand the Dirichlet form of the boundary process. 相似文献
20.
HE PING YING JIANGANG Institute of Mathematics Fudan Univeraity Shanghai China. Institute of Mathematics Fudan University Shanghai China. 《数学年刊B辑(英文版)》2003,(4)
In this paper, the authors investigate the joint distribution of end points of excursion away from a closed set straddling on a fixed time and use this result to compute the Levy system and the Dirichlet form of the boundary process. 相似文献