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1.
2.
《随机分析与应用》2013,31(4):755-782
In this paper, we use the Riemann sum approach to construct the anticipative stochastic integrals and consider the Cauchy problem (non-adapted initial value) for stochastic integral equations driven by discontinuous semimartingales. For general equations with Lipschitz coefficients, we prove the existence of the solutions. Apropos of semilinear equations, we find that under some conditions uniqueness of solutions will also hold. 相似文献
3.
Jiongmin Yong 《Probability Theory and Related Fields》1997,107(4):537-572
Summary. The notion of bridge is introduced for systems of coupled forward–backward stochastic differential equations (FBSDEs, for short). This notion
helps us to unify the method of continuation in finding adapted solutions to such FBSDEs over any finite time durations. It is proved that if two FBSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several
classes of uniquely solvable FBSDEs.
Received: 23 April 1996 / In revised form: 10 October 1996 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.
6.
Olivier Raimond 《Probability Theory and Related Fields》1997,107(2):177-196
Summary. In this paper we study a self-attracting diffusion in the case of a constant self-attraction and for dimension larger than
two. We prove that this process converges almost surely.
Received: 27 March 1995 / In revised form: 22 May 1996 相似文献
7.
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
8.
9.
Summary. We consider a continuous model for transverse magnetization of spins diffusing in a homogeneous Gaussian random longitudinal
field , where is the coupling constant giving the intensity of the random field. In this setting, the transverse magnetization is given
by the formula , where is the standard process of Brownian motion and is the covariance function of the original random field . We use large deviation techniques to show that the limit exists. We also determine the small behavior of the rate and show that it is indeed decaying as conjectured in the physics literature.
Received: 30 June 1995 / In revised form: 26 January 1996 相似文献
10.
OSCILLATIONTHEOREMSFORSECONDORDERNONLINEARDELAYDIFFERENTIALEQUATIONSJinMingzhong(靳明忠)(WuhanInstituteofTechnology)Abstract:Som... 相似文献
11.
Carl Mueller 《Probability Theory and Related Fields》1998,110(1):51-68
Summary. Let ? be the circle [0,J] with the ends identified. We prove long-time existence for the following equation.
Here, =(t,x) is 2-parameter white noise, and we assume that u
0(x) is a continuous function on ?. We show that if g(u) grows no faster than C
0(1+|u|)γ for some γ<3/2, C
0>0, then this equation has a unique solution u(t,x) valid for all times t>0.
Received: 27 November 1996 / In revised form: 28 July 1997 相似文献
12.
13.
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
14.
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
15.
We consider symmetric simple exclusion processes with L=&ρmacr;N
d
particles in a periodic d-dimensional lattice of width N. We perform the diffusive hydrodynamic scaling of space and time. The initial condition is arbitrary and is typically far
away form equilibrium. It specifies in the scaling limit a density profile on the d-dimensional torus. We are interested in the large deviations of the empirical process, N
−
d
[∑
L
1δ
xi
(·)] as random variables taking values in the space of measures on D[0.1]. We prove a large deviation principle, with a rate function that is more or less universal, involving explicity besides
the initial profile, only such canonical objects as bulk and self diffusion coefficients.
Received: 7 September 1997 / Revised version: 15 May 1998 相似文献
16.
ANOSCILLATIONCRITERIONFORSECONDORDERSUBLINEARDIFFERENTIALEQUATIONS¥LiWantong(ZhangyeTeachers'College,734000)QuanHongshun(Lanz... 相似文献
17.
In this paper,we obtain suffcient conditions for the stability in p-th moment of the analytical solutions and the mean square stability of a stochastic differential equation with unbounded delay proposed in [6,10] using the explicit Euler method. 相似文献
18.
R. A. Doney 《Probability Theory and Related Fields》1997,107(4):451-465
Summary. If {S
n
,n≧0} is an integer-valued random walk such that S
n
/a
n
converges in distribution to a stable law of index α∈ (0,1) as n→∞, then Gnedenko’s local limit theorem provides a useful estimate for P{S
n
=r} for values of r such that r/a
n
is bounded. The main point of this paper is to show that, under certain circumstances, there is another estimate which is
valid when r/a
n
→ +∞, in other words to establish a large deviation local limit theorem. We also give an asymptotic bound for P{S
n
=r} which is valid under weaker assumptions. This last result is then used in establishing some local versions of generalized
renewal theorems.
Received: 9 August 1995 / In revised form: 29 September 1996 相似文献
19.
Let X
i
, i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z
n
= E (exp (n
Φ (∑
i
=1
n
X
i
/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without
the central limit theorem assumption.
Received: 19 September 1997 / Revised version:22 April 1999 相似文献
20.
Erwan Saint Loubert Bié 《Probability Theory and Related Fields》1998,111(2):287-321
Résumé . Nous étudions une équation aux dérivées partielles stochastique (EDPS), de type parabolique, posée sur ℝ
d
, d entier, et conduite par un bruit poissonnien, compensé ou non. La première partie de ce travail montre l'existence et l'unicité
d'une solution progressivement mesurable. Les techniques employées sont proches de celles utilisées pour résoudre les équations
analogues conduites par un bruit blanc. La seconde partie donne des conditions, portant sur l'intensité du bruit poissonnien,
et permettant d'assurer certaines régularités, en espace ou bien en temps, pour le processus solution.
Summary. We study a Stochastic Partial Differential Equation, of parabolic type, set on ℝ d , with d∈ℕ. This equation is driven by a Poisson random measure, either compensated or not. The first part of this work shows existence and uniqueness of a progressively measurable solution. The technics involved are close to those used to deal with analogous equations driven by a Gaussian noise. The second part gives some criterions on the intensity of the Poisson random measure, in order to ensure some smoothness, either in space or in time, for the solution of this equation.
Received: 7 April 1997/In revised form: 20 January 1998 相似文献