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1.
In this paper,we study the stochastic partial differential equation with two reflecting smooth walls h^1 and h^2,driven by a fractional noise,which is fractional in time and white in space.The large deviation principle for the law of the solution to this equation,will be established through developing a classical method.Furthermore,we obtain the H?lder continuity of the solution.  相似文献   

2.
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponentially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.  相似文献   

3.
We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As an application,we establish a large deviation principle of the Freidlin and Wentzell type under the corresponding nonlinear probability for diffusion processes with a small diffusion coefficient.  相似文献   

4.
Riccati equation approach is used to look for exact travelling wave solutions of some nonlinear physical models.Solitary wave solutions are established for the modified KdV equation,the Boussinesq equation and the Zakharov-Kuznetsov equation.New generalized solitary wave solutions with some free parameters are derived.The obtained solutions,which includes some previously known solitary wave solutions and some new ones,are expressed by a composition of Riccati differential equation solutions followed by a polynomial.The employed approach,which is straightforward and concise,is expected to be further employed in obtaining new solitary wave solutions for nonlinear physical problems.  相似文献   

5.
In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method.  相似文献   

6.
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.  相似文献   

7.
A Property of <Emphasis Type="Italic">g</Emphasis>-Expectation   总被引:6,自引:0,他引:6  
This paper proves that, under the hypothesis g(t, 0, 0) ≡ 0 and some natural assumptions, the generator g of a backward stochastic differential equation can be uniquely determined by the corresponding g-expectations with all terminal conditions. The main result of this paper also confirms and extends Peng Shige‘s conjecture.  相似文献   

8.
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.  相似文献   

9.
We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.  相似文献   

10.
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.  相似文献   

11.
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.  相似文献   

12.
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward–backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman–Kac formula to the non-Markovian framework.  相似文献   

13.
本文研究一类由分数布朗运动驱动的一维倒向随机微分方程解的存在性与唯一性问题,在假设其生成元满足关于y Lipschitz连续,但关于z一致连续的条件下,通过应用分数布朗运动的Tanaka公式以及拟条件期望在一定条件下满足的单调性质,得到倒向随机微分方程的解的一个不等式估计,应用Gronwall不等式得到了一个关于这类方程的解的存在性与唯一性结果,推广了一些经典结果以及生成元满足一致Lipschitz条件下的由分数布朗运动驱动的倒向随机微分方程解的结果.  相似文献   

14.
In this paper, we study Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games via the theory of backward stochastic differential equations. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games with nonlinear cost functionals defined with the help of doubly controlled backward stochastic differential equations. Our results extend former ones by Buckdahn et al. (2004) [3] and are based on a backward stochastic differential equation approach.  相似文献   

15.
 In this paper we study a class of one-dimensional, degenerate, semilinear backward stochastic partial differential equations (BSPDEs, for short) of parabolic type. By establishing some new a priori estimates for both linear and semilinear BSPDEs, we show that the regularity and uniform boundedness of the adapted solution to the semilinear BSPDE can be determined by those of the coefficients, a special feature that one usually does not expect from a stochastic differential equation. The proof follows the idea of the so-called bootstrap method, which enables us to analyze each of the derivatives of the solution under consideration. Some related results, including some comparison theorems of the adapted solutions for semilinear BSPDEs, as well as a nonlinear stochastic Feynman-Kac formula, are also given. Received: 16 January 2001 / Revised version: 11 October 2001 / Published online: 14 June 2002  相似文献   

16.
This article shows that the solution of a backward stochastic differential equation under G-expectation provides a probabilistic interpretation for the viscosity solution of a type of path-dependent Hamilton-Jacobi-Bellman equation. Particularly, a G-martingale can be considered as a nonlinear path-dependent partial differential equation (PDE). We also show that certain class of path-dependent PDEs can be transformed into classical multiple state-dependent PDEs. As an application, the path-dependent uncertain volatility model can be described directly by path-dependent Black-Scholes-Barrenblett equations.  相似文献   

17.
首先,针对一类线性倒向随机微分方程,给出了g-鞅同鞅之间相互联系所满足的充分条件.通过该条件得到了经典的Black-Scholes模型下未定权益的公平价格过程以及最优增长投资策略的价格过程.其次,引入了带惩罚的非线性倒向随机微分方程,并通过惩罚比率的不同取值来讨论相关的经济学意义.  相似文献   

18.
Abstract

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain.  相似文献   

19.
A nonlinear stochastic evolution equation in Hilbert space with generalized additive white noise is considered. A concept of stochastic mertial manifold is introduced, defined as a random manifold depending on time, which is finite dimensional, invariant for the dynamic, and attracts exponentially fast all the trajectories as t → ∞. Under the classical spectral gap condition of the deterministic theory, the existence of a stochastic inertial manifold is proved. It is obtained as the solution of a stochastic partial differential equation of degenerate parabolic type, studied by a variant of Bernstein method. A result of existence and uniqueness of a stationary inertial manifold is also proved; the stationary inertial manifold contains the random attractor, introduced in previous works.  相似文献   

20.
In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.  相似文献   

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