共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider non-linear stochastic functional differential equations (sfde's) on Euclidean space. We give sufficient conditions for the sfde to admit locally compact smooth cocycles on the underlying infinite-dimensional state space. Our construction is based on the theory of finite-dimensional stochastic flows and a non-linear variational technique. In Part II of this article, the above result will be used to prove a stable manifold theorem for non-linear sfde's. 相似文献
2.
We state and prove a Local Stable Manifold Theorem (Theorem 4.1) for non-linear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary trajectories of sfde's. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary trajectory. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques developed by D. Ruelle, together with interpolation arguments. 相似文献
3.
Summary. We study a new class of backward stochastic differential equations, which involves the integral with respect to a continuous
increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial differential equations
with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic
equations.
Received: 27 September 1996 / In revised form: 1 December 1997 相似文献
4.
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
5.
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
6.
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
7.
S. Taniguchi 《Probability Theory and Related Fields》1999,114(3):291-308
An evaluation of a stochastic oscillatory integral with quadratic phase function and analytic amplitude function is given
by using solutions of Jacobi equations. The evaluation will be obtained as an application of real change of variable formulas
and holomorphic prolongations of analytic functions on a real Wiener space. On the way we shall see how a Jacobi equation
appears in the evaluation by using the Malliavin calculus.
Received: 27 July 1998 / Revised version: 14 October 1998 相似文献
8.
We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with
random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the
Skorohod integral deduced from It?'s formula for this anticipating stochastic integral.
Received: 21 November 1997 / Revised version: 20 July 1998 相似文献
9.
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
10.
Ito's rule is established for the diffusion processes on the graphs. We also consider a family of diffusions processes with
small noise on a graph. Large deviation principle is proved for these diffusion processes and their local times at the vertices.
Received: 12 February 1997 / Revised version: 3 March 1999 相似文献
11.
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
12.
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
13.
Antoine Lejay 《Probability Theory and Related Fields》2001,120(2):255-276
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization
property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic
random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients
are non-degeneracy and boundedness.
Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001 相似文献
14.
By replacing the final condition for backward stochastic differential equations (in short: BSDEs) by a stationarity condition
on the solution process we introduce a new class of BSDEs. In a natural manner we associate to such BSDEs the periodic solution
of second order partial differential equations with periodic structure.
Received: 11 October 1996 / Revised version: 15 February 1999 相似文献
15.
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
16.
Here we study the α-stability for holomorphic triples over curves of genus g = 1. We provide necessary and sufficient conditions for the moduli space of α-stable triples to be non-empy and, in these cases, we show that it is smooth and irreducible.
Received: January 10, 2007. 相似文献
17.
We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words
of length N from an alphabet of k letters. (In the limit as k→∞ these become the corresponding distributions for permutations on N letters.) We find Toeplitz determinant representations for the exponential generating functions (on N) of these distribution functions and show that they are expressible in terms of solutions of Painlevé V equations. We show
further that in the weakly increasing case the generating unction gives the distribution of the smallest eigenvalue in the
k×k Laguerre random matrix ensemble and that the distribution itself has, after centering and normalizing, an N→∞ limit which is equal to the distribution function for the largest eigenvalue in the Gaussian Unitary Ensemble of k×k hermitian matrices of trace zero.
Received: 9 September 1999 / Revised version: 24 May 2000 / Published online: 24 January 2001 相似文献
18.
Lars Larsson-Cohn 《Monatshefte für Mathematik》2002,137(1):51-56
We study the growth of the constants in the Meyer inequality as p → 1 and p → ∞. Both constants grow, within constant factors, like (p − 1)−1 and like p respectively.
Received August 10, 2001; in revised form February 5, 2002 相似文献
19.
Multiple fractional integrals 总被引:2,自引:0,他引:2
Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly
identified.
Received: 23 February 1998 / Revised version: 31 July 1998 相似文献
20.
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