共查询到20条相似文献,搜索用时 31 毫秒
1.
Sigurd Assing 《Probability Theory and Related Fields》2001,120(2):143-167
The paper deals with the infinite-dimensional stochastic equation dX= B(t, X) dt + dW driven by a Wiener process which may also cover stochastic partial differential equations. We study a certain finite dimensional
approximation of B(t, X) and give a qualitative bound for its rate of convergence to be high enough to ensure the weak uniqueness for solutions of
our equation. Examples are given demonstrating the force of the new condition.
Received: 6 November 1999 / Revised version: 21 August 2000 / Published online: 6 April 2001 相似文献
2.
Hirofumi Osada 《Probability Theory and Related Fields》2001,119(2):275-310
We construct a family of diffusions P
α = {P
x} on the d-dimensional Sierpinski carpet F^. The parameter α ranges over d
H
< α < ∞, where d
H
= log(3
d
− 1)/log 3 is the Hausdorff dimension of the d-dimensional Sierpinski carpet F^. These diffusions P
α are reversible with invariant measures μ = μ[α]. Here, μ are Radon measures whose topological supports are equal to F^ and satisfy self-similarity in the sense that μ(3A) = 3α·μ(A) for all A∈ℬ(F^). In addition, the diffusion is self-similar and invariant under local weak translations (cell translations) of the
Sierpinski carpet. The transition density p = p(t, x, y) is locally uniformly positive and satisfies a global Gaussian upper bound. In spite of these well-behaved properties, the
diffusions are different from Barlow-Bass' Brownian motions on the Sierpinski carpet.
Received: 30 September 1999 / Revised version: 15 June 2000 / Published online: 24 January 2000 相似文献
3.
We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the
bond dilute Ising model on ℤ
d
at inverse temperature β. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any β, with probability one, the spectral gap
of the generator of the dyamics in a box of side L centered at the origin scales like L
−2. Such an estimate is then used to prove a decay to equilibrium for local functions of the form where ε is positive and arbitrarily small and α = ? for d = 1, α=1 for d≥2. In particular our result shows that, contrary to what happes for the Glauber dynamics, there is no dynamical phase transition
when β crosses the critical value β
c
of the pure system.
Received: 10 April 2000 / Revised version: 23 October 2000 / Published online: 5 June 2001 相似文献
4.
Endre Csáki Miklós Csörgő Antónia Földes Zhan Shi 《Probability Theory and Related Fields》2000,117(4):515-531
Let W be a standard Brownian motion, and define Y(t)= ∫0
t
ds/W(s) as Cauchy's principal value related to local time. We determine: (a) the modulus of continuity of Y in the sense of P. Lévy; (b) the large increments of Y.
Received: 1 April 1999 / Revised version: 27 September 1999 / Published online: 14 June 2000 相似文献
5.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Probability Theory and Related Fields》1998,111(2):253-286
Summary. We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian behaviour for the weakly self-avoiding
walk on ℤ
d
where loops of length m are penalised by a factor e
−β/m p
(0<β≪1) when: (1) d>4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0.
Received: 29 October 1997 / In revised form: 15 January 1998 相似文献
6.
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
7.
M.S. Bernabei 《Probability Theory and Related Fields》2001,119(3):410-432
The Central Limit Theorem for a model of discrete-time random walks on the lattice ℤν in a fluctuating random environment was proved for almost-all realizations of the space-time nvironment, for all ν > 1 in
[BMP1] and for all ν≥ 1 in [BBMP]. In [BMP1] it was proved that the random correction to the average of the random walk for
ν≥ 3 is finite. In the present paper we consider the cases ν = 1,2 and prove the Central Limit Theorem as T→∞ for the random correction to the first two cumulants. The rescaling factor for theaverage is for ν = 1 and (ln T), for ν=2; for the covariance it is , ν = 1,2.
Received: 25 November 1999 / Revised version: 7 June 2000 / Published online: 15 February 2001 相似文献
8.
Andreas Greven Achim Klenke Anton Wakolbinger 《Probability Theory and Related Fields》2001,120(1):85-117
We study the longtime behaviour of interacting systems in a randomly fluctuating (space–time) medium and focus on models
from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and
interacting Fisher–Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is
proportional to a random environment (catalytic medium).
Here we introduce a model of interacting Fisher–Wright diffusions where the local resampling rate (or genetic drift) is proportional
to a catalytic medium. For a particular choice of the medium, we investigate the longtime behaviour in the case of nearest
neighbour migration on the d-dimensional lattice.
While in classical homogeneous systems the longtime behaviour exhibits a dichotomy along the transience/recurrence properties
of the migration, now a more complicated behaviour arises. It turns out that resampling models in catalytic media show phenomena
that are new even compared with branching in catalytic medium.
Received: 15 November 1999 / Revised version: 16 June 2000 / Published online: 6 April 2001 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.
Sandra Cerrai 《Probability Theory and Related Fields》1999,113(1):85-114
In the present paper we consider the transition semigroup P
t
related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in
the Banach space of continuous functions , where ⊂ℝ
d
is a bounded open set. In L
2() the only result proved is the strong Feller property, for d=1. Here we are able to prove that if f∈C
∞(ℝ) and d≤3, then for any and t>0. An important application is to the study of the ergodic properties of the system. These results are also of interest for
some problem in stochastic control.
Received: 20 August 1997 / Revised version: 27 May 1998 相似文献
11.
Nobuo Yoshida 《Probability Theory and Related Fields》1999,115(1):1-40
We consider a ferromagnetic spin system with unbounded interactions on the d-dimensional integer lattice (d > 1). Under mild assumptions on the one-body interactions (so that arbitrarily deep double wells are allowed), we prove that
if the coupling constants are small enough, then the finite volume Gibbs states satisfy the log-Sobolev inequality uniformly
in the volume and the boundary condition.
Received: 11 November 1997 / Revised version: 17 July 1998 相似文献
12.
Werner Georg Nowak 《Monatshefte für Mathematik》2002,137(3):227-238
This article is concerned with sums 𝒮(t) = ∑
n
ψ(tf(n/t)) where ψ denotes, essentially, the fractional part minus ?, f is a C
4-function with f″ ≠ 0 throughout, summation being extended over an interval of order t. We establish an asymptotic formula for ∫
T−Λ
T+Λ
(𝒮(t))2dt for any Λ = Λ(T) growing faster than log T.
Received April 30, 2001; in revised form February 15, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
13.
Summary. We introduce a new family of first-passage percolation (FPP) models in the context of Poisson-Voronoi tesselations of ℝ
d
. Compared to standard FPP on ℤ
d
, these models have some technical complications but also have the advantage of statistical isotropy. We prove two almost
sure results: a shape theorem (where isotropy implies an exact Euclidean ball for the asymptotic shape) and nonexistence of
certain doubly infinite geodesics (where isotropy yields a stronger result than in standard FPP).
Received: 21 May 1996 / In revised form: 19 November 1996 相似文献
14.
Tokuzo Shiga 《Probability Theory and Related Fields》1997,108(3):417-439
Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;
d
in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate
the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.
Received: 21 May 1996 / In revised form: 2 February 1997 相似文献
15.
Jean-Stéphane Dhersin Jean-François Le Gall 《Probability Theory and Related Fields》1997,108(1):103-129
We prove a Wiener-type criterion for super-Brownian motion and the Brownian snake.If F is a Borel subset of ℝ
d
and x ∈ ℝ
d
, we provide a necessary and sufficientcondition for super-Brownian motion started at δ
x
to immediately hit the set F. Equivalently, this condition is necessary and sufficient for the hitting time of F by theBrownian snake with initial point x to be 0. A key ingredient of the proof isan estimate showing that the hitting probability of F is comparable, up to multiplicative constants,to the relevant capacity of F. This estimate, which is of independent interest, refines previous results due to Perkins and Dynkin. An important role is
played by additivefunctionals of the Brownian snake, which are investigated here via the potentialtheory of symmetric Markov
processes. As a direct application of our probabilisticresults, we obtain a necessary and sufficient condition for the existence
in a domain D of a positivesolution of the equation Δ; u = u
2
which explodes at a given point of ∂ D.
Received: 5 January 1996 / In revised form: 30 October 1996 相似文献
16.
Summary. We consider the Cauchy problem for the mass density ρ of particles which diffuse in an incompressible fluid. The dynamical
behaviour of ρ is modeled by a linear, uniformly parabolic differential equation containing a stochastic vector field. This
vector field is interpreted as the velocity field of the fluid in a state of turbulence. Combining a contraction method with
techniques from white noise analysis we prove an existence and uniqueness result for the solution ρ∈C
1,2([0,T]×ℝ
d
,(S)*), which is a generalized random field. For a subclass of Cauchy problems we show that ρ actually is a classical random field,
i.e. ρ(t,x) is an L
2-random variable for all time and space parameters (t,x)∈[0,T]×ℝ
d
.
Received: 27 March 1995 / In revised form: 15 May 1997 相似文献
17.
Wei-Min Wang 《Probability Theory and Related Fields》2001,119(4):453-474
We further develop the supersymmetric formalism initiated in [W1] (see also [SjW]). We obtain the optimal mean field bounds
at the critical energy for Lyapunov exponents of random walks in random potentials in Z
d
at weak disorder. This extends some of the results in [W1].
Received: 9 December 1999 / Revised version: 8 May 2000 /?Published online: 15 February 2001 相似文献
18.
Feng-Yu Wang 《Probability Theory and Related Fields》1997,108(1):87-101
Summary. This paper presents some explicit lower bound estimates of logarithmic Sobolev constant for diffusion processes on a compact
Riemannian manifold with negative Ricci curvature. Let Ric≧−K for some K>0 and d, D be respectively the dimension and the diameter of the manifold. If the boundary of the manifold is either empty or convex,
then the logarithmic Sobolev constant for Brownian motion is not less than
max
{(d d+2)
d
1 2(d+1)D
2
exp
[−1−(3d+2)D
2
K], (d−1 d+1)
d
K
exp
[−4D√d K]} .
Next, the gradient estimates of heat semigroups (including the Neumann heat semigroup and the Dirichlet one) are studied by
using coupling method together with a derivative formula modified from [11]. The resulting estimates recover or improve those
given in [7, 21] for harmonic functions.
Received: 19 September 1995 / In revised form 11 April 1996 相似文献
19.
Hydrodynamic large scale limit for the Ginzburg-Landau ∇φ interface model was established in [6]. As its next stage this
paper studies the corresponding large deviation problem. The dynamic rate functional is given by
for h=h(t,θ),t∈[0,T],θ∈?
d
, where σ=σ(u) is the surface tension for mean tilt u∈ℝ
d
. Our main tool is H
−1-method expoited by Landim and Yau [9]. The relationship to the rate functional obtained under the static situation by Deuschel
et al. [3] is also discussed.
Received: 22 February 2000 / Revised version: 19 October 2000 / Published online: 5 June 2001 相似文献
20.
Consider a d-dimensional Brownian motion X = (X
1,…,X
d
) and a function F which belongs locally to the Sobolev space W
1,2. We prove an extension of It? s formula where the usual second order terms are replaced by the quadratic covariations [f
k
(X), X
k
] involving the weak first partial derivatives f
k
of F. In particular we show that for any locally square-integrable function f the quadratic covariations [f(X), X
k
] exist as limits in probability for any starting point, except for some polar set. The proof is based on new approximation
results for forward and backward stochastic integrals.
Received: 16 March 1998 / Revised version: 4 April 1999 相似文献