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1.
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
2.
在生成元~$g$~的第~$i$~个分量~$g_i(t,y,z)$~仅仅依赖于矩阵~$z$~的第~$i$
行的条件下, Hamad\`{e}ne于2003年证明了生成元一致连续的倒向随机微分
方程的~$L^2$~解的存在性, 其~$L^2$~解的唯一性由范胜君等于2010年得到. 本文进一步地证明了该类倒向随机微分
方程的~$L^p\ (p>1)$~解的存在唯一性. 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.
This paper aims at solving a multidimensional backward stochastic differential equation (BSDE) whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results. 相似文献
6.
7.
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
8.
In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the associated BSDE does not admit any bounded solution. On the other hand, we prove that if the superquadratic BSDE admits a bounded solution, then there exist infinitely many bounded solutions for this BSDE. Finally, we prove the existence of a solution for Markovian BSDEs where the terminal value is a bounded continuous function of a forward stochastic differential equation. 相似文献
9.
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
10.
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
11.
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
12.
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
13.
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
14.
《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
15.
2003年Briand et al等在很一般的假设下建立了倒向随机微分方程(BSDEs)L^p解的存在唯一性定理.本文在此基础上得到了这种假设下一维BSDEs的L^p解的几个连续性质. 相似文献
16.
In this paper, we establish the existence of the minimal L~p(p 1) solution of backward stochastic differential equations(BSDEs) where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {(Y~n, Z~n)} which is a Cauchy sequence in S~p× M~p space, and finally we prove {(Y~n, Z~n)} converges to the L~p(p 1) solution of BSDEs. 相似文献
17.
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
18.
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
19.
LongJiang 《应用数学学报(英文版)》2004,20(4):701-706
With the help of a limit property of solutions of backward stochastic differential equations(BSDEs),this paper establishes a converse comparison theorem for deterministic generators g of BSDEs under the assumption g(t, y, 0) ≡0. 相似文献
20.
Kahled Bahlali M. Hassani B. Mansouri N. Mrhardy 《Comptes Rendus Mathematique》2009,347(19-20):1201-1206
We prove the existence and uniqueness of solutions to Reflected Backward Doubly Stochastic Differential Equations (RBDSDEs) with one continuous barrier and uniformly Lipschitz coefficients. The existence of a maximal and a minimal solution for RBDSDEs with continuous generator is also established. To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献