共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on
a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples
of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Received: 6 July 1999 / Revised version: 19 April 2000 /?Published online: 14 June 2001 相似文献
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
11.
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
12.
M. Zähle 《Probability Theory and Related Fields》1998,111(3):333-374
The classical Lebesgue–Stieltjes integral ∫
b
a
fdg of real or complex-valued functions on a finite interval (a,b) is extended to a large class of integrands f and integrators g of unbounded variation. The key is to use composition formulas and integration-by-part rules for fractional integrals and
Weyl derivatives. In the special case of H?lder continuous functions f and g of summed order greater than 1 convergence of the corresponding Riemann–Stieltjes sums is proved.
The results are applied to stochastic integrals where g is replaced by the Wiener process and f by adapted as well as anticipating random functions. In the anticipating case we work within Slobodeckij spaces and introduce
a stochastic integral for which the classical It? formula remains valid. Moreover, this approach enables us to derive calculation
rules for pathwise defined stochastic integrals with respect to fractional Brownian motion.
Received: 14 January 1998 / Revised version: 9 April 1998 相似文献
13.
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
14.
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
15.
This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate,
continuous dependence on a parameter) of forward–backward stochastic differential equations and their connection with quasilinear
parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward equation to be degenerate.
Received: 12 May 1997 / Revised version: 10 January 1999 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.
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
18.
For ν(dθ), a σ-finite Borel measure on R
d
, we consider L
2(ν(dθ))-valued stochastic processes Y(t) with te property that Y(t)=y(t,·) where y(t,θ)=∫
t
0
e
−λ(θ)(
t
−
s
)
dm(s,θ) and m(t,θ) is a continuous martingale with quadratic variation [m](t)=∫
t
0
g(s,θ)ds. We prove timewise H?lder continuity and maximal inequalities for Y and use these results to obtain Hilbert space regularity for a class of superrocesses as well as a class of stochastic evolutions
of the form dX=AXdt+GdW with W a cylindrical Brownian motion. Maximal inequalities and H?lder continuity results are also provenfor the path process
t
(τ)≗Y(τt∧t).
Received: 25 June 1999 / Revised version: 28 August 2000 /?Published online: 9 March 2001 相似文献
19.
On the long time behavior of the stochastic heat equation 总被引:2,自引:0,他引:2
We consider the stochastic heat equation in one space dimension and compute – for a particular choice of the initial datum
– the exact long time asymptotic. In the Carmona-Molchanov approach to intermittence in non stationary random media this corresponds
to the identification of the sample Lyapunov exponent. Equivalently, by interpreting the solution as the partition function of a directed polymer in a random environment, we obtain
a weak law of large numbers for the quenched free energy. The result agrees with the one obtained in the physical literature
via the replica method. The proof is based on a representation of the solution in terms of the weakly asymmetric exclusion
process.
Received: 11 November 1997 / Revised version: 31 July 1998 相似文献
20.
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