共查询到20条相似文献,搜索用时 31 毫秒
1.
Wendelin Werner 《Probability Theory and Related Fields》1994,99(1):111-144
Résumé Nous étudions le comportement asymptotique de l'aireA
n
de l'ensemble des points autour desquels le mouvement brownien plan a tourné environn fois sur un intervalle de temps fixé [0,t]. Nous montrons en particulier que lorsquen tend vers l'infini,A
n
est équivalent dansL
2 àt/(2n
2) asn
Summary We study the asymptotic behaviour of the areaA n of the set of points around which the planar Brownian motion winds about n times on a given timeinterval [0,t]. We prove thatA n is equivalent (in theL 2-sense) tot/(2n 2) asn tends to infinity.相似文献
2.
André Goldman 《Probability Theory and Related Fields》1996,105(1):57-83
Résumé The spectral empirical function of a homogeneous, isotropic, Poisson mosaic process is a functional of the perimeter of the convex hull of planar Brownian bridge. Some geometrical identities follow.
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3.
Wendelin Werner 《Probability Theory and Related Fields》1994,98(3):307-337
Résumé Nous nous proposons d'étudier la forme des petites composantes connexes du complémentaire de la trajectoire brownienne plane. Nous montrons l'existence d'une loi limite de cette forme. De plus, nous obtenons un théorème limite qui montre que la donnée de l'ensemble des composantes connexes correspondant à une seule trajectoire suffit pour décrire cette loi.
Summary We study the shape of the small connected components of the complement of a 2-dimensional Brownian path. We show the existence of an asymptotic law for this shape. Moreover, we prove a limit theorem that shows that the family of all the connected components of the complement of a single path contains all the information about this law.相似文献
4.
5.
Jean Bertoin 《Probability Theory and Related Fields》1993,96(1):123-135
Summary We study the behaviour of a Lévy process with no positive jumps near its increase times. Specifically, we construct a local time on the set of increase times. Then, we describe the path decomposition at an increase time chosen at random according to the local time, and we evaluate the rate of escape before and after this instant. 相似文献
6.
We consider a semilinear partial differential equation (PDE) of non-divergence form perturbed by a small parameter. We then study the asymptotic behavior of Sobolev solutions in the case where the coefficients admit limits in C?esaro sense. Neither periodicity nor ergodicity will be needed for the coefficients. In our situation, the limit (or averaged or effective) coefficients may have discontinuity. Our approach combines both probabilistic and PDEs arguments. The probabilistic one uses the weak convergence of solutions of backward stochastic differential equations (BSDE) in the Jakubowski S-topology, while the PDEs argument consists to built a solution, in a suitable Sobolev space, for the PDE limit. We finally show the existence and uniqueness for the associated averaged BSDE, then we deduce the uniqueness of the limit PDE from the uniqueness of the averaged BSDE. 相似文献
7.
Lucien Chevalier 《Journal of Functional Analysis》2004,207(2):344-357
In our previous papers (Adv. in Math. 138 (1) (1998) 182; Potential Anal. 12 (2000) 419), we have obtained a decomposition of |f|, where f is a function defined on , that is analogous to the one proved by H. Tanaka for martingales (the so-called “Tanaka formula”). More precisely, the decomposition has the form , where is (a variant of ) the density of the area integral associated with f. This functional (introduced by R.F. Gundy in his 1983 paper (The density of area integral, Conference on Harmonic Analysis in Honor of Antoni Zygmund. Wadsworth, Belmont, CA, 1983, pp. 138-149.)) can be viewed as the counterpart of the local time in Euclidean harmonic analysis. In this paper, we are interested in boundedness and continuity properties of the mapping (which we call the Lévy transform in analysis) on some classical function or distribution spaces. As was shown in [4,5], the above (non-linear) decomposition is bounded in Lp for every p∈[1,+∞[, i.e. one has , where Cp is a constant depending only on p. Nevertheless our methods (roughly speaking, the Calderón-Zygmund theory in [4], stochastic calculus and martingale inequalities in [5]) both gave constants Cp whose order of magnitude near 1 is O(1/(p−1)). The aim of this paper is two-fold: first, we improve the preceding result and we answer a natural question, by proving that the best constants Cp are bounded near 1. Second, we prove that the Lévy transform is continuous on the Hardy spaces Hp with p>n/(n+1). 相似文献
8.
Edwin Perkins 《Probability Theory and Related Fields》1992,94(2):189-245
Summary A strong equation driven by a historical Brownian motion is used to construct and characterize measure-valued branching diffusions in which the spatial motions obey an Itô equation with drift and diffusion depending on the position of an individual and the entire population. 相似文献
9.
Summary We obtain sharp (i.e. non logarithmic) asymptotics for the solution of non homogeneous Kolmogorov-Petrovski-Piskunov equation depending on a small parameter , for points ahead of the Freidlin-KPP front. 相似文献
10.
A superprocess limit for an interacting birth-death particle system modeling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not hold. We use a martingale problem approach and a separation of the slow (trait) and fast (age) scales. While the trait marginals converge in a pathwise sense to a superprocess, the age distributions, on another time scale, average to equilibria that depend on traits. The convergence of the whole process depending on trait and age, only holds for finite-dimensional time-marginals. We apply our results to the study of examples illustrating different cases of trade-off between competition and senescence. 相似文献
11.
12.
L. Overbeck 《Probability Theory and Related Fields》1993,96(4):545-570
Summary We investigate classes of conditioned super-Brownian motions, namely H-transformsP
H
with non-negative finitely-based space-time harmonic functionsH(t, ). We prove thatH
H
is the unique solution of a martingale problem with interaction and is a weak limit of a sequence of rescaled interacting branching Brownian motions. We identify the limit behaviour of H-transforms with functionsH(t, )=h(t, (1)) depending only on the total mass (1). Using the Palm measures of the super-Brownian motion we describe for an additive spacetime harmonic functionH(t, )=h(t, x) (dx) theH-transformP
H
as a conditioned super-Brownian motion in which an immortal particle moves like an h-transform of Brownian motion. 相似文献
13.
14.
15.
Summary In this work we study the absolute continuity of the image of the Wiener measure under the transformations of the formT()=+u(), the shiftu is a random variable with values in the Cameron-Martin spaceH and is monotone in the sense that (T(+h-T(),h)
H
0 a.s. for allh inH. 相似文献
16.
We consider a class of multitype particle systems in
d
undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria). 相似文献
17.
18.
Some dimension results for super-Brownian motion 总被引:4,自引:0,他引:4
Laurent Serlet 《Probability Theory and Related Fields》1995,101(3):371-391
Summary The Dawson-Watanabe super-Brownian motion has been intensively studied in the last few years. In particular, there has been much work concerning the Hausdorff dimension of certain remarkable sets related to super-Brownian motion. We contribute to this study in the following way. Let (Y
t)t0 be a super-Brownian motion on
d
(d2) andH be a Borel subset of
d
. We determine the Hausdorff Dimension of {t0; SuppY
tHØ}, improving and generalizing a result of Krone. We also obtain a new proof of a result of Tribe which gives, whend4, the Hausdorff dimension of
SuppY
t
as a function of the dimension ofB. 相似文献
19.
Farid Madani 《Bulletin des Sciences Mathématiques》2008,132(7):575
Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation
20.
Toshiro Watanabe 《Probability Theory and Related Fields》1996,104(3):349-374
Summary We consider increasing processes {X(t)t0} of classL, that is, increasing self-similar processes with inswpendent increments. Leth(t) be an increasing positive function on (0,) withh(0+)=0 andh()=. By virtue of the zero-one laws, there existsc (resp.C) [0,] such that lim inf (resp. lim sup)X(t)/h(t)=c (resp.C) a.s. both ast tends to 0 and ast tends to . We decide a necessary and sufficient condition for the existence ofh(t) withc orC=1 and explicitly constructh(t) in caseh(t) exists withc orC=1. Moreover, we give a criterion to classify functionsh(t) withc (orC)=0 andh(t) withc (orC)= in caseh(t) does not exist withc (orC)=1. 相似文献