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1.
If C
1 is the convex hull of the curve of a standard Brownian motion in the complex plane watched from 0 to 1, we consider the convex
hulls of C
1 and several rotations of it and compute the mean of the length of their perimeter by elementary calculations. This can be
seen geometrically as a study of the exit time by a Brownian motion from certain polytopes having the unit circle as an inscribed
one. 相似文献
2.
A. N. Borodin 《Journal of Mathematical Sciences》2008,152(6):853-861
We consider a Brownian motion with jumps that is a sum of a Brownian motion and compound Poisson process. It is assumed that
the distribution of jumps is symmetrically exponential. A formula for the Laplace transform of the distribution of time spent
by a Brownian motion with jumps over some level is obtained. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 101–116. 相似文献
3.
Mario Abundo 《随机分析与应用》2017,35(3):499-510
We find explicit formulae for the mean of the running maximum of conditional and unconditional Brownian motion; they are used to obtain the mean, a(t), of the running maximum of an integrated Gauss–Markov process. Then, we deal with the connection between the moments of its first-passage-time and a(t). As explicit examples, we consider integrated Brownian motion and integrated Ornstein–Uhlenbeck process. 相似文献
4.
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
5.
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion
started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and
the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional
Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this
Bessel bridge stays below some fixed value. 相似文献
6.
Strong approximations in a charged-polymer model 总被引:1,自引:0,他引:1
We study the large-time behavior of the charged-polymer Hamiltonian H n of Kantor and Kardar [Bernoulli case] and Derrida, Griffiths, and Higgs [Gaussian case], using strong approximations to Brownian motion. Our results imply, among other things, that in one dimension the process {H [nt]}0≤t≤1 behaves like a Brownian motion, time-changed by the intersection local-time process of an independent Brownian motion. Chung-type LILs are also discussed. 相似文献
7.
Ming Liao 《Journal of Theoretical Probability》1999,12(2):475-488
We consider isometric stochastic flows on the sphere S
n–1 with the same one point motion. In particular, we will show that when n>3, the set of such flows with Brownian motion as one point motion can be represented by a cube in some Euclidean space. 相似文献
8.
V. Metz 《Potential Analysis》2007,26(2):121-137
On the bounded Sierpinski gasket F we use the set of essential fixed points V
0 as a boundary and consider the fractal Brownian motion on F killed in V
0. The corresponding Dirichlet–Laplacian is described in terms of a kind of hyperbolic distance, a metric which explodes near
the boundary. We consider Harnack inequalities, Green’s function estimates and (random) products of matrices defining the
local energy of harmonic functions.
Supported by the DFG research group ‘Spektrale Analysis, asymptotische Verteilungen und stochastische Dynamik.’ 相似文献
9.
Jean-François Delmas 《Probability Theory and Related Fields》1999,114(4):505-547
We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting
behavior of the volume of the ɛ-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous
result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove
the support of X
t
is capacity-equivalent to [0, 1]2 in ℝd, d≥ 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1]4 in ℝd, d≥ 5.
Received: 7 April 1998 / Revised version: 2 October 1998 相似文献
10.
We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments. 相似文献
11.
We find the optimal investment strategy to minimize the expected time that an individual’s wealth stays below zero, the so-called
occupation time. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and
one risky asset, with the risky asset’s price process following a geometric Brownian motion. We also consider an extension
of this problem by penalizing the occupation time for the degree to which wealth is negative. 相似文献
12.
13.
Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H
n
, n > 2. For ν > 0, the Brownian bridge B
(ν) of length ν on H is the process B
t
, 0 ≤t≤ν, conditioned by B
0 = B
ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge
on ℝ3). The same result holds for the simple random walk on an homogeneous tree.
Received: 4 December 1998 / Revised version: 22 January 1999 相似文献
14.
Nathalie Eisenbaum 《Probability Theory and Related Fields》1997,107(4):527-535
Summary. At time t, the most visited site of a linear Brownian motion is defined as the point which realises the supremum of the local times
at time t. Let V be the time indexed process of the most visited sites by a linear Brownian motion. We show that every value is polar for
V. Those results are extended from Brownian motion to symmetric stable processes, and then to the absolute value of a symmetric
stable process.
Received: 1 March 1996 / In revised form: 17 October 1996 相似文献
15.
A. N. Borodin 《Probability Theory and Related Fields》1986,72(2):231-250
Summary Many results are known about the convergence of some processes to Brownian local time. Among such processes are the process of occupation times of Brownian motion, the number of downcrossings of Brownian motion over smaller and smaller intervals before timet, the number of visits of the recurrent integer-valued random walk to some point duringn steps and others. In this paper we consider the asymptotic behaviour of the differences between Brownian local time and some of the processes which converge to it. 相似文献
16.
R. Abraham L. Serlet 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):287-308
We consider a path-valued process which is a generalization of the classical Brownian snake introduced by Le Gall. More precisely we add a drift term b to the lifetime process, which may depends on the spatial process. Consequently, this introduces a coupling between the lifetime process and the spatial motion. This process can be obtained from the standard Brownian snake by Girsanov's theorem or by killing of the spatial motion. It can also be viewed as the limit of discrete snakes or, in some special cases, as conditioned Brownian snakes. We also use this process to describe the solutions of the non-linear partial differential equation j u =4 u 2 +4 bu . 相似文献
17.
Wensheng Wang 《Probability Theory and Related Fields》2003,126(2):203-220
Kesten and Spitzer have shown that certain random walks in random sceneries converge to stable processes in random sceneries.
In this paper, we consider certain random walks in sceneries defined using stationary Gaussian sequence, and show their convergence
towards a certain self-similar process that we call fractional Brownian motion in Brownian scenery.
Received: 17 April 2002 / Revised version: 11 October 2002 /
Published online: 15 April 2003
Research supported by NSFC (10131040).
Mathematics Subject Classification (2002): 60J55, 60J15, 60J65
Key words or phrases: Weak convergence – Random walk in random scenery – Local time – Fractional Brownian motion in Brownian scenery 相似文献
18.
Jason Swanson 《Probability Theory and Related Fields》2007,138(1-2):269-304
We consider the median of n independent Brownian motions, denoted by M n (t), and show that $\sqrt{n}\,M_nWe consider the median of n independent Brownian motions, denoted by M
n
(t), and show that
converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through
direct estimates on the increments of the median process. An explicit formula is given for the covariance function of the
limit process. The limit process is also shown to be H?lder continuous with exponent γ for all γ < 1/4.
相似文献
19.
T. Sottinen 《Journal of Theoretical Probability》2004,17(2):309-325
We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H1/2. For the case H>1/2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation we consider a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise. 相似文献
20.
Small ball probability is estimated for a Brownian motion in l
p. As an application we establish the modulus of non-differentiability of a Brownian motion in l
p.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献