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.
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
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.
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
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.
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
7.
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
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.
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
10.
Espen R. Jakobsen Kenneth H. Karlsen 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(2):137-165
We formulate and prove a non-local “maximum principle for semicontinuous functions” in the setting of fully nonlinear and
degenerate elliptic integro-partial differential equations with integro operators of second order. Similar results have been
used implicitly by several researchers to obtain compare/uniqueness results for integro-partial differential equations, but
proofs have so far been lacking. 相似文献
11.
Pao-Liu Chow Ildar A. Ibragimov Rafail Z. Khasminskii 《Probability Theory and Related Fields》1999,113(3):421-441
For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric
estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate
the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity
tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence is
ascertained within a wide class of risk functions in a minimax sense.
Received: 5 May 1997 / Revised version: 18 June 1998 相似文献
12.
In this paper we prove Lp estimates (p≥2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic
type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear
parabolic PDE. 相似文献
13.
Summary. By coupling two arbitrary riemannian connections Γ and Γ˜ on a riemannian manifold M, we perform the stochastic calculus of ɛ-variation on the path space P(M) of the manifold M. The method uses direct calculations on Ito’s stochastic differential equations. In this context, we obtain intertwinning
formulas with the Ito map for first order operators on the path space P(M) of M. By a judicious choice of the second connection Γ˜ in terms of the connection Γ, we can prolongate the intertwinning formulas to second order differential operators. Thus, we obtain expressions of heat
operators on the path space P(M) of a riemannian manifold M endowed with an arbitrary connection. The integration by parts of the laplacians on P(M) leads us to the notion of dilatation vector field on the path space.
Received: 18 April 1995 / In revised form: 18 March 1996 相似文献
14.
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
15.
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
16.
We give general conditions on a generator of a C0-semigroup (resp. of a C0-resolvent) on Lp(E,μ), p ≥ 1, where E is an arbitrary (Lusin) topological space and μ a σ-finite measure on its Borel σ-algebra, so that it generates a sufficiently
regular Markov process on E. We present a general method how these conditions can be checked in many situations. Applications to solve stochastic differential
equations on Hilbert space in the sense of a martingale problem are given.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
17.
This paper is devoted to forward-backward systems of stochastic differential equations in which the forward equation is not
coupled to the backward one, both equations are infinite dimensional and on the time interval [0, + ∞). The forward equation
defines an Ornstein-Uhlenbeck process, the driver of the backward equation has a linear part which is the generator of a strongly
continuous, dissipative, compact semigroup, and a nonlinear part which is assumed to be continuous with linear growth. Under
the assumption of equivalence of the laws of the solution to the forward equation, we prove the existence of a solution to
the backward equation. We apply our results to a stochastic game problem with infinitely many players. 相似文献
18.
Shige Peng 《Probability Theory and Related Fields》1999,113(4):473-499
We have obtained the following limit theorem: if a sequence of RCLL supersolutions of a backward stochastic differential
equations (BSDE) converges monotonically up to (y
t
) with E[sup
t
|y
t
|2] < ∞, then (y
t
) itself is a RCLL supersolution of the same BSDE (Theorem 2.4 and 3.6).
We apply this result to the following two problems: 1) nonlinear Doob–Meyer Decomposition Theorem. 2) the smallest supersolution
of a BSDE with constraints on the solution (y, z). The constraints may be non convex with respect to (y, z) and may be only measurable with respect to the time variable t. this result may be applied to the pricing of hedging contingent claims with constrained portfolios and/or wealth processes.
Received: 3 June 1997 / Revised version: 18 January 1998 相似文献
19.
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
20.
Andrzej Rozkosz 《Probability Theory and Related Fields》2003,125(3):393-407
We extend the definition of solutions of backward stochastic differential equations to the case where the driving process
is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of
solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic
partial differential equations in Sobolev spaces.
Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002
Research supported by KBN Grant 0253 P03 2000 19.
Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55
Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution 相似文献