共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
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
3.
Michelle Boué Paul Dupuis Richard S. Ellis 《Probability Theory and Related Fields》2000,116(1):125-149
This paper proves the large deviation principle for a class of non-degenerate small noise diffusions with discontinuous drift
and with state-dependent diffusion matrix. The proof is based on a variational representation for functionals of strong solutions
of stochastic differential equations and on weak convergence methods.
Received: 26 May 1998 / Revised version: 24 February 1999 相似文献
4.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional
and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed
into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting
of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give
sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are
applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise.
Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
5.
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
6.
Nathanaël Enriquez Jacques Franchi Yves Le Jan 《Probability Theory and Related Fields》2001,119(2):213-255
Let ℳ be a geometrically finite hyperbolic surface with infinite volume, having at least one cusp. We obtain the limit law
under the Patterson-Sullivan measure on T
1ℳ of the windings of the geodesics of ℳ around the cusps. This limit law is stable with parameter 2δ− 1, where δ is the Hausdorff
dimension of the limit set of the subgroup Γ of M?bius isometries associated with ℳ. The normalization is t
−1/(2δ−1), for geodesics of length t. Our method relies on a precise comparison between geodesics and diffusion paths, for which we need to approach the Patterson-Sullivan
measure mentioned above by measures that are regular along the stable leaves.
Received: 8 October 1999 / Revised version: 2 June 2000 / Published online: 21 December 2000 相似文献
7.
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
8.
A nonparametric statistical model of small diffusion type is compared with its discretization by a stochastic Euler difference
scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's deficiency
distance for statistical experiments, when the discretization step decreases with the noise intensity ε.
Received: 12 April 1996 / Revised version: 29 October 1997 相似文献
9.
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
10.
Emmanuel Rio 《Probability Theory and Related Fields》2001,119(2):163-175
We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on
entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large
deviations rate function of a binomial law in most of the cases.
Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000 相似文献
11.
Wu Liming 《Probability Theory and Related Fields》1999,114(4):549-585
Let ℒ≔Δ/2+(∇φ/φ) ·∇ be a generalized Schr?dinger operator or generator of Nelsons diffusion, defined on C
∞
0(D) where φ is a continuous and strictly positive function on an open domain D⊂ℝ
d
such that ∇φ∈L
loc
2(D). Some results are given about the two questions below: (i) Whether does ℒ generate a unique semigroup in L
1(D, φ2
dx)? (ii) Whether the semigroup determined by ℒ is strong Feller?
Received: 21 October 1997 / Revised version: 3 September 1998 相似文献
12.
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
13.
Crossing estimates for symmetric Markov processes 总被引:2,自引:0,他引:2
A crossing estimate is established for symmetric Markov processes on general state spaces.
Received: 20 May 1999 / Revised version: 30 August 2000 / Published online: 9 March 2001 相似文献
14.
We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept
allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function
technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application,
we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations for
the corresponding invariant measures. Our general theorems yield a priori estimates and existence results for such elliptic
equations. We also obtain moment estimates for Gibbs distributions and prove an existence result applicable to a wide class
of models.
Received: 23 January 2000 / Revised version: 4 October 2000 / Published online: 5 June 2001 相似文献
15.
John Hawkes 《Probability Theory and Related Fields》1998,112(1):1-11
Exact results are proved for the capacity of pullbacks of analytic sets by stable processes.
Received: 25 May 1988 / Revised version: 15 September 1997 相似文献
16.
We say that n independent trajectories ξ1(t),…,ξ
n
(t) of a stochastic process ξ(t)on a metric space are asymptotically separated if, for some ɛ > 0, the distance between ξ
i
(t
i
) and ξ
j
(t
j
) is at least ɛ, for some indices i, j and for all large enough t
1,…,t
n
, with probability 1. We prove sufficient conitions for asymptotic separationin terms of the Green function and the transition
function, for a wide class of Markov processes. In particular,if ξ is the diffusion on a Riemannian manifold generated by
the Laplace operator Δ, and the heat kernel p(t, x, y) satisfies the inequality p(t, x, x) ≤ Ct
−ν/2 then n trajectories of ξ are asymptotically separated provided . Moreover, if for some α∈(0, 2)then n trajectories of ξ(α) are asymptotically separated, where ξ(α) is the α-process generated by −(−Δ)α/2.
Received: 10 June 1999 / Revised version: 20 April 2000 / Published online: 14 December 2000
RID="*"
ID="*" Supported by the EPSRC Research Fellowship B/94/AF/1782
RID="**"
ID="**" Partially supported by the EPSRC Visiting Fellowship GR/M61573 相似文献
17.
Eberhard Mayerhofer 《Stochastic Processes and their Applications》2011,121(9):2072-2086
We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics.Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the αth positive semidefinite power of the process itself with 0.5<α<1 and obtain existence conditions for them. In the case of a diffusion coefficient which is linear in the process we likewise get a positive definite analogue of the univariate GARCH diffusions. 相似文献
18.
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
19.
We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges
to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and
Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics.
Received: 2 February 1998 / Revised version: 28 August 1998 相似文献
20.
For 2-D stochastic Navier-Stokes equations on the torus with multiplicative noise we construct a perfect cocycle and show
the existence of global random compact attractors. The equations considered do not admit a pathwise method of solution.
Received: 9 June 1998 / Revised version: 17 December 1998 相似文献