共查询到20条相似文献,搜索用时 312 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.
We consider a mechanical model in the plane, consisting of a vertical rod, subject to a constant horizontal force f and to elastic collisions with the particles of a free gas which is “horizontally” in equilibrium at some inverse temperature
β. In a previous paper we proved that, in the appropriate space and time scaling, the motion of the rod is described as a drift
term plus a diffusion term. In this paper we prove that the drift d(f) and the diffusivity σ
2
(f) are continuous functions of f, and moreover that the Einstein relation holds, i.e.,
lim
f → 0
d(f)f = β2 σ
2
(0) .
Received: 26 January 1996 / In revised form: 2 October 1996 相似文献
3.
For a bounded C
1,α domain in ℝ
d
we show that there exists a strong solution to the multidimensional Skorokhod equation and that weak uniqueness holds for
this equation. These results imply that pathwise uniqueness and strong uniqueness hold for the Skorokhod equation.
Received: 3 February 1999 / Revised version: 2 September 1999 /?Published online: 11 April 2000 相似文献
4.
Kenneth S. Alexander 《Probability Theory and Related Fields》1998,110(4):441-471
Summary. For lattice models on ℤ
d
, weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance
from that region. For a wide class of models on ℤ2, including all finite range models, we show that weak mixing is a consequence of Gibbs uniqueness, exponential decay of an
appropriate form of connectivity, and a natural coupling property. In particular, on ℤ2, the Fortuin-Kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially,
and the q-state Potts model above the critical temperature is weak mixing whenever correlations decay exponentially, a hypothesis satisfied
if q is sufficiently large. Ratio weak mixing is the property that uniformly over events A and B occurring on subsets Λ and Γ, respectively, of the lattice, |P(A∩B)/P(A)P(B)−1| decreases exponentially in the distance between Λ and Γ. We show that under mild hypotheses, for example finite range,
weak mixing implies ratio weak mixing.
Received: 27 August 1996 / In revised form: 15 August 1997 相似文献
5.
Hiroshi Kaneko 《Probability Theory and Related Fields》2000,117(4):533-550
In this paper, we will give sufficient conditions for the existence of the reflecting diffusion process on a locally compact
space. In constructing reflecting diffusion process, we consider the corresponding Martin–Kuramochi boundary as the reflecting
barrier and introduce the notion of strong (ℰ, u)-Caccioppoli set. Our method covers reflecting diffusion processes with diffusion coefficient degenerating on the boundary.
Received: 23 June 1997 / Revised version: 28 September 1991/ Published online: 14 June 2000 相似文献
6.
We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities
introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated
with a computable set A, {e : W
e
≤
q
u
A} for q∈ {m, T} are Σ4
0 complete. We also show hat FPT(≤
q
n
), that is {e : W
e
computable and ≡
q
n
?}, is Σ4
0 complete. We also look at computable presentability of these classes.
Received: 13 July 1996 / Revised version: 14 April 2000 / Published online: 18 May 2001 相似文献
7.
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
8.
In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new
a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity
of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical
finance.
Received: 24 September 1997 / Revised version: 3 June 1998 相似文献
9.
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
10.
Andreas Eberle 《Probability Theory and Related Fields》1997,109(1):77-99
Summary. We construct Ornstein–Uhlenbeck processes and more general diffusion processes on path and loop spaces of Riemannian manifolds
by finite dimensional approximation. We also show H?lder continuity of the sample paths w.r.t. the supremum norm. The proofs
are based on the Lyons–Zheng decomposition.
Received: 6 September 1996 / In revised form: 1 April 1997 相似文献
11.
Hideki Tanemura 《Probability Theory and Related Fields》1997,109(2):275-299
Summary. Dirichlet forms associated with systems of infinitely many Brownian balls in ℝ
d
are studied. Introducing a linear operator L
0 defined on a space of smooth local functions, we show the uniqueness of Dirichlet forms associated with self adjoint Markovian
extensions of L
0. We also discuss the ergodicity of the reversible process associated with the Dirichlet form.
Received: 18 July 1996/In revised form: 13 February 1997 相似文献
12.
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
13.
S. B. Damelin 《Monatshefte für Mathematik》2003,138(2):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities.
Received April 4, 2001; in final form June 21, 2002 相似文献
14.
The L
p
minimax risks (1≤p<∞) are studied for statistical estimation in the Gaussian white noise model. The asymptotic rate and constants are given,
and the optimal estimator is proposed. This, together with the work of Golubev, Levit and Tsybakov (1996) establishes the
classification of the L
p
minimax constants on the classes of analytical functions.
Received: 10 December 1996 / Revised version: 14 December 1997 相似文献
15.
Wendelin Werner 《Probability Theory and Related Fields》1997,108(1):131-152
Summary. We study the asymptotic behaviour of disconnection and non-intersection exponents for planar Brownian motionwhen the number
of considered paths tends to infinity. In particular, if η
n
(respectively ξ (n, p)) denotes the disconnection exponent for n paths (respectively the non-intersection exponent for n paths versus p paths), then we show that lim
n →∞
η
n
/n = 1 2 and that for a > 0 and b > 0,lim
n →∞
ξ ([na],[nb])/n = (√ a + √ b)
2
/2.
Received: 28 February 1996 / In revised form: 3 September 1996 相似文献
16.
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
17.
Sompolinski and Zippelius (1981) propose the study of dynamical systems whose invariant measures are the Gibbs measures for
(hard to analyze) statistical physics models of interest. In the course of doing so, physicists often report of an “aging”
phenomenon. For example, aging is expected to happen for the Sherrington-Kirkpatrick model, a disordered mean-field model
with a very complex phase transition in equilibrium at low temperature. We shall study the Langevin dynamics for a simplified
spherical version of this model. The induced rotational symmetry of the spherical model reduces the dynamics in question to
an N-dimensional coupled system of Ornstein-Uhlenbeck processes whose random drift parameters are the eigenvalues of certain random
matrices. We obtain the limiting dynamics for N approaching infinity and by analyzing its long time behavior, explain what is aging (mathematically speaking), what causes
this phenomenon, and what is its relationship with the phase transition of the corresponding equilibrium invariant measures.
Received: 8 July 1999 / Revised version: 2 June 2000 / Published online: 6 April 2001 相似文献
18.
Summary. Let (W, H, μ) be an abstract Wiener space and let Tw = w + u (w), where u is an H-valued random variable, be a measurable transformation on W. A Sard type lemma and a degree theorem for this setup are presented and applied to derive existence of solutions to elliptic
stochastic partial differential equations.
Received: 19 March 1996 / In revised form: 7 January 1997 相似文献
19.
We present an upper bound O(n
2
) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant,
and find tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion
process on a circle indeed mixes more rapidly than the corresponding symmetric process.
Received: 25 January 1999 / Revised version: 17 September 1999 / Published online: 14 June 2000 相似文献
20.
For a wide class of local martingales (M
t
) there is a default function, which is not identically zero only when (M
t
) is strictly local, i.e. not a true martingale. This default in the martingale property allows us to characterize the integrability
of functions of sup
s≤t
M
s
in terms of the integrability of the function itself. We describe some (paradoxical) mean-decreasing local sub-martingales,
and the default functions for Bessel processes and radial Ornstein–Uhlenbeck processes in relation to their first hitting
and last exit times.
Received: 6 August 1996 / Revised version: 27 July 1998 相似文献