共查询到20条相似文献,搜索用时 31 毫秒
1.
《Stochastic Processes and their Applications》2002,102(2):285-299
We establish new Kahane–Khintchine inequalities in Orlicz spaces induced by exponential Young functions for stationary real random fields which are bounded or satisfy some finite exponential moment condition. Next, we give sufficient conditions for partial sum processes indexed by classes of sets satisfying some metric entropy condition to converge in distribution to a set-indexed Brownian motion. Moreover, the class of random fields that we study includes φ-mixing and martingale difference random fields. 相似文献
2.
Consider a stochastic process that lives on n-semiaxes emanating from a common origin. On each semiaxis it behaves as a Brownian motion and at the origin it chooses a semiaxis randomly. In this paper we study the first hitting time of the process. We derive the Laplace transform of the first hitting time, and provide the explicit expressions for its density and distribution functions. Numerical examples are presented to illustrate the application of our results.
相似文献3.
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at \(-\infty \) . We show that these processes do not have to have the distribution of standard Brownian motion in the backward direction of time, no matter which random time we take as the origin. We study the maximum and minimum rates of growth for these processes in the backward direction. We also address the question of which extra assumptions make one of these processes a two-sided Brownian motion. 相似文献
4.
In this paper we study harmonic functions of subordinate killed Brownian motion in a domain D. We first prove that, when the killed Brownian semigroup in D is intrinsic ultracontractive, all nonnegative harmonic functions of the subordinate killed Brownian motion in D are continuous and then we establish a Harnack inequality for these harmonic functions. We then show that, when D is a bounded Lipschitz domain, both the Martin boundary and the minimal Martin boundary of the subordinate killed Brownian motion in D coincide with the Euclidean boundary ∂D. We also show that, when D is a bounded Lipschitz domain, a boundary Harnack principle holds for positive harmonic functions of the subordinate killed Brownian motion in D. 相似文献
5.
B. L. S. Prakasa Rao 《随机分析与应用》2013,31(6):1203-1215
Abstract We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion. 相似文献
6.
B. L. S. Prakasa Rao 《随机分析与应用》2018,36(4):600-612
We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by a sub-fractional Brownian motion. 相似文献
7.
In this paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional
Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we
furthermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1],
a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai
type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordingly.
The method can actually be applied to a larger class of Gaussian processes with covariance functions satisfying a simple decay
condition.
Received: 11 May 2000 / Revised version: 20 March 2001 / Published online: 11 December 2001 相似文献
8.
Alexandre Richard 《Journal of Theoretical Probability》2017,30(4):1285-1309
We obtain a spectral representation and compute the small ball probabilities for a (non-increment stationary) multiparameter extension of the fractional Brownian motion. We derive from these results a Chung-type law of the iterated logarithm at the origin and exhibit the singular behaviour of this multiparameter fractional Brownian motion, as it behaves very differently at the origin and away from the axes. A functional version of this Chung-type law is also provided. 相似文献
9.
A. de Acosta 《Probability Theory and Related Fields》2000,118(4):483-521
We prove an abstract large deviation result for a sequence of random elements of a vector space satisfying an “abstract exponential
martingale condition”. The framework naturally generates non-convex rate functions. We apply the result to solutions of It?
stochastic equations in R
d
driven by Brownian motion and a Poisson random measure.
Received: 23 June 1999 / Revised version: 17 February 2000 / Published online: 22 November 2000 相似文献
10.
11.
B. L. S. Prakasa Rao 《随机分析与应用》2013,31(5):767-781
ABSTRACTWe investigate the asymptotic properties of the maximum likelihood estimator and Bayes estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by a mixed fractional Brownian motion. We obtain a Bernstein–von Mises-type theorem also for such a class of processes. 相似文献
12.
B. L. S. Prakasa Rao 《随机分析与应用》2017,35(6):943-953
We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by mixed fractional Brownian motion. 相似文献
13.
The modulus of continuity of a stochastic process is a random element for any fixed mesh size. We provide upper bounds for the moments of the modulus of continuity of Itô processes with possibly unbounded coefficients, starting from the special case of Brownian motion. References to known results for the case of Brownian motion and Itô processes with uniformly bounded coefficients are included. As an application, we obtain the rate of strong convergence of Euler–Maruyama schemes for the approximation of stochastic delay differential equations satisfying a Lipschitz condition in supremum norm. 相似文献
14.
Wolfgang Bock Jos Luís da Silva Ludwig Streit 《Mathematical Methods in the Applied Sciences》2019,42(18):7452-7460
In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution. 相似文献
15.
Raphaël Forien 《Stochastic Processes and their Applications》2019,129(10):3748-3773
We study a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. We obtain a non trivial scaling limit which behaves like reflected Brownian motion until its local time at zero reaches an exponential variable. It then follows reflected Brownian motion on the other side of the origin until its local time at zero reaches another exponential level, etc. These random walks are used in population genetics to trace the position of ancestors in the past near geographical barriers. 相似文献
16.
In this paper, a new class of backward doubly stochastic differential equations driven by Teugels martingales associated with a Lévy process satisfying some moment condition and an independent Brownian motion is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given. 相似文献
17.
S. Albeverio P. E. T. Jorgensen A. M. Paolucci 《Complex Analysis and Operator Theory》2012,6(1):33-63
Given a fractional Brownian motion (fBm) with Hurst index H ? (0,1){H\in(0,1)} , we associate with this a special family of representations of Cuntz algebras related to frequency domains and wavelets.
Vice versa, we consider a pair of Haar wavelets satisfying some compatibility conditions, and we construct the covariance
functions of fBm with a fixed Hurst index. The Cuntz algebra representations enter the picture as filters of the associated
wavelets. Extensions to q-dependent covariance functions leading to a corresponding fBm process will also be discussed. 相似文献
18.
We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for the case wherein the particles have a positive probability of having no children. Then using this tool, we obtain results regarding the asymptotic behavior of the number of particles above λt at time t for λ>0. Under an L log L condition, we prove a strong law of large numbers for this catalytic branching Brownian motion. 相似文献
19.
R. A. Doney Y. B. Nakhi 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2001,37(6):737
In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and lower functions of the supremum as t→∞. In the Brownian case these include extensions of recent results in Lambert [4], but are proved in a quite different way. 相似文献
20.
Zoran Vondraček 《Journal of Theoretical Probability》2000,13(1):279-309
We study the asymptotic behavior of the first-passage times for Brownian motion, Lévy processes and continuous martingales over one-sided increasing stochastic, as well as deterministic, boundaries. In particular, we study the first-passage time of a Brownian motion over the increasing function of its local time, give necessary and sufficient conditions for t
–1/2 asymptotics, and obtain exact asymptotics for linear functions. 相似文献