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1.
This paper is interested in solving a multidimensional backward stochastic differential equation (BSDE) whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results. 相似文献
2.
ShengJun Fan Long Jiang DeJian Tian 《Stochastic Processes and their Applications》2011,121(3):427-440
This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators. 相似文献
3.
Existence,uniqueness and approximation for <Emphasis Type="Italic">L</Emphasis><Superscript>p</Superscript> solutions of reflected BSDEs with generators of one-sided Osgood type 下载免费PDF全文
Sheng Jun Fan 《数学学报(英文版)》2017,33(6):807-838
We prove several existence and uniqueness results for L p (p > 1) solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works. 相似文献
4.
In this paper we study the existence and uniqueness of L p (p>1) solutions for one-dimensional backward stochastic differential equations (BSDEs in short) whose generator g and terminal condition ?? satisfy $\mathbf{E}[|\xi|^{p}+(\int_{0}^{T} |g(t,0,0)|\, \mathrm {d}t)^{p}]<+\infty$ . We get an existence result under the condition that g is continuous and of linear growth in (y,z). And, we also prove an existence and uniqueness result where g satisfies the Osgood condition in y and is uniformly continuous in z. Particularly, a comparison theorem for L p (p>1) solutions of BSDEs is obtained in this paper. 相似文献
5.
In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables y and z. The aim of this paper is to extend these results to the case of a generator satisfying a monotonicity condition in y. More precisely, we prove existence and uniqueness for 2BSDEs with a generator which is Lipschitz in z and uniformly continuous with linear growth in y. Moreover, we emphasize throughout the paper the major difficulties and differences due to the 2BSDE framework. 相似文献
6.
Mingyu Xu 《Journal of Theoretical Probability》2007,20(4):1005-1039
In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity
and general increasing condition on y, with Lipschitz condition on z. 相似文献
7.
In this paper, we establish a general representation theorem for generator of backward stochastic differential equation (BSDE), whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation. 相似文献
8.
《Stochastic Processes and their Applications》2003,108(1):109-129
In this paper, we are interested in solving backward stochastic differential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions in Lp p>1, extending the results of El Karoui et al. (Math. Finance 7(1) (1997) 1) to the case where the monotonicity conditions of Pardoux (Nonlinear Analysis; Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic Publishers, Dordrecht, pp. 503–549) are satisfied. We consider both a fixed and a random time interval. In the last section, we obtain, under an additional assumption, an existence and uniqueness result for BSDEs on a fixed time interval, when the data are only in L1. 相似文献
9.
This paper is devoted to the $L^p$ ($p>1$) solutions of
one-dimensional backward stochastic differential equations (BSDEs
for short) with general time intervals and generators satisfying
some non-uniform conditions in $t$ and $\omega$. An existence and
uniqueness result, a comparison theorem and an existence result for
the minimal solutions are respectively obtained, which considerably
improve some known works. Some classical techniques used to deal
with the existence and uniqueness of $L^p$ ($p>1$) solutions of
BSDEs with Lipschitz or linear-growth generators are also developed
in this paper. 相似文献
10.
Qing Zhou 《应用数学学报(英文版)》2010,26(2):333-344
In this paper we study reflected and doubly reflected backward stochastic differential equations (BSDEs, for short) driven by Teugels martingales associated with L~vy process satisfying some moment condi- tions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the Tanaka-Meyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski's condition by using the Snell envelope theory and then we obtain a comparison result. 相似文献
11.
Existence,Uniqueness and Approximation for L~p Solutions of Reflected BSDEs with Generators of One-sided Osgood Type 下载免费PDF全文
《数学学报(英文版)》2017,(6)
We prove several existence and uniqueness results for L~p(p 1) solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z.A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works. 相似文献
12.
《Applied Mathematics Letters》2002,15(6):735-741
By using a fixed-point theorem in G-convex spaces due to the first author, an existence result for abstract nonlinear inequalities without any monotonicity assumptions is established. As a consequence of our result, we obtain some further generalizations of recent known results. As application, an existence theorem for perturbed saddle point problems is obtained in noncompact G-convex spaces. 相似文献
13.
This paper is devoted to real valued backward stochastic differential equations (BSDEs for short) with generators which satisfy a stochastic Lipschitz condition involving BMO martingales. This framework arises naturally when looking at the BSDE satisfied by the gradient of the solution to a BSDE with quadratic growth in Z. We first prove an existence and uniqueness result from which we deduce the differentiability with respect to parameters of solutions to quadratic BSDEs. Finally, we apply these results to prove the existence and uniqueness of a mild solution to a parabolic partial differential equation in Hilbert space with nonlinearity having quadratic growth in the gradient of the solution. 相似文献
14.
In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity. 相似文献
15.
Guangyan Jia 《Comptes Rendus Mathematique》2006,342(9):685-688
In this Note, we deal with one-dimensional backward stochastic differential equations (BSDEs) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z, but without explicit growth constraint. We prove, in this setting, an existence theorem for backward stochastic differential equations. To cite this article: G. Jia, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
16.
In Briand and Hu (Probab Theory Relat Fields 136(4):604–618, 2006), the authors proved an existence result for BSDEs with
quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper
is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex
with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates
stated in Karoui et al. (Math Finance 7(1):1–71, 1997). With these tools in hands, we can derive the nonlinear Feynman–Kac
formula in this context. 相似文献
17.
The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to (f,δ)-expectations induced by anticipated BSDEs. 相似文献
18.
《Nonlinear Analysis: Theory, Methods & Applications》2004,59(7):1091-1124
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In our previous work a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper we extend this generic existence and uniqueness result to a class of optimal control problems in which the right-hand side of differential equations is also subject to variations. 相似文献
19.
This paper establishes a generalized comparison theorem for one-dimensional backward stochastic differential equations (BSDEs)
whose generators are uniformly continuous in z and satisfy a kind of weakly monotonic condition in y. As applications, two new existence and uniqueness theorems for solutions of BSDEs are obtained. In the one-dimensional setting,
these results generalize some corresponding results in Pardoux and Peng (Syst. Control Lett. 14:55–61, 1990), Mao (Stoch. Process. Their Appl. 58:281–292, 1995), El Karoui et al. (Math. Finance 7:1–72, 1997), Pardoux (Nonlinear Analysis, Differential Equations and Control, Montreal, QC, 1998, Kluwer Academic, Dordrecht, 1999), Cao and Yan (Adv. Math. 28(4):304–308, 1999), Briand and Hu (Probab. Theory Relat. Fields 136(4):604–618, 2006), and Jia (C. R. Acad. Sci. Paris, Ser. I 346:439–444, 2008). 相似文献
20.
林清泉 《数学物理学报(A辑)》2004,4(5):589-596
作者讨论非Lipschitz条件下g 上鞅的非线性Doob Meyer 分解. 为此讨论一类漂移系数g(s,·,·)关于(y,z)不满足Lipschitz条
件的倒向随机微分方程解的存在唯一性,运用Biharis不等式证明了一类倒向随机微分方程的比较定理以及g 上解的极限定理. 相似文献