共查询到20条相似文献,搜索用时 15 毫秒
1.
Qian Lin 《Applied mathematics and computation》2011,217(22):9322-9333
In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain existence theorems and comparison theorems for solutions of BDSDEs with weak assumptions on the coefficients. 相似文献
2.
Summary We introduce a new class of backward stochastic differential equations, which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations, thus extending the Feynman-Kac formula for linear SPDE's.The research of this author was partially supported by DRET under contract 901636/A000/DRET/DS/SRThe research of this author was supported by a grant from the French Ministère de la Recherche et de la Technologie, which is gratefully acknowledged 相似文献
3.
This paper is concerned with the weak solution (in analytic sense) to the Cauchy–Dirichlet problem of a backward stochastic partial differential equation when the nonhomogeneous term has a quadratic growth in both the gradient of the first unknown and the second unknown. Existence and uniqueness results are obtained under separate conditions. 相似文献
4.
Ying Hu Yiqing Lin Abdoulaye Soumana Hima 《Stochastic Processes and their Applications》2018,128(11):3724-3750
In this paper, we consider backward stochastic differential equations driven by -Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the -framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces. 相似文献
5.
For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe
how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines.
We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of
the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the
experimental data.
March 29, 2000. Date revised: March 6, 2001. Date accepted: March 21, 2001. 相似文献
6.
Naoyuki Ichihara 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3):243-266
We discuss homogenization for stochastic partial differential equations (SPDEs) of Zakai type with periodic coefficients appearing typically in nonlinear filtering problems. We prove such homogenization by two different approaches. One is rather analytic and the other is comparatively probabilistic. 相似文献
7.
Maximum density for the Sierpinski gasket 总被引:1,自引:0,他引:1
In the paper we show that there exists a closed convex set attaining the maximum density for the Sierpinski gasket. 相似文献
8.
Backward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A duality principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the duality principle, a comparison theorem is proved for the adapted solutions of BSVIEs, and a Pontryagin type maximum principle is established for an optimal control of stochastic integral equations. 相似文献
9.
In [R. Buckdahn, B. Djehiche, J. Li, S. Peng, Mean-field backward stochastic differential equations. A limit approach. Ann. Probab. (2007) (in press). Available online: http://www.imstat.org/aop/future_papers.htm] the authors obtained mean-field Backward Stochastic Differential Equations (BSDE) associated with a mean-field Stochastic Differential Equation (SDE) in a natural way as a limit of a high dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “agents”). The objective of the present paper is to deepen the investigation of such mean-field BSDEs by studying them in a more general framework, with general coefficient, and to discuss comparison results for them. In a second step we are interested in Partial Differential Equations (PDE) whose solutions can be stochastically interpreted in terms of mean-field BSDEs. For this we study a mean-field BSDE in a Markovian framework, associated with a McKean–Vlasov forward equation. By combining classical BSDE methods, in particular that of “backward semigroups” introduced by Peng [S. Peng, J. Yan, S. Peng, S. Fang, L. Wu (Eds.), in: BSDE and Stochastic Optimizations; Topics in Stochastic Analysis, Science Press, Beijing (1997) (Chapter 2) (in Chinese)], with specific arguments for mean-field BSDEs, we prove that this mean-field BSDE gives the viscosity solution of a nonlocal PDE. The uniqueness of this viscosity solution is obtained for the space of continuous functions with polynomial growth. With the help of an example it is shown that for the nonlocal PDEs associated with mean-field BSDEs one cannot expect to have uniqueness in a larger space of continuous functions. 相似文献
10.
In this paper, we are interested in real-valued backward stochastic differential equations with jumps together with their applications to non-linear expectations. The notion of non-linear expectations has been studied only when the underlying filtration is given by a Brownian motion and in this work the filtration will be generated by both a Brownian motion and a Poisson random measure. We study at first backward stochastic differential equations driven by a Brownian motion and a Poisson random measure and then introduce the notions of f-expectations and of non-linear expectations in this set-up. 相似文献
11.
Backward stochastic differential equation with random measures 总被引:5,自引:0,他引:5
夏建明 《应用数学学报(英文版)》2000,16(3):225-234
1. IntroductionPardoux and Peng[1], Peng[2'3] have discussed backward stochastic differential equations(BSDE) driven by Brownian motioll. Tangl4], Tang and Li[5] have considered BSDEdriven by Brownian motion and Poisson process. We will extend many results of them inthis paper.The main reference is [6].Let (fi, F, (R),P) be a filtered probability space, where the filtration (R) satisfies theusual conditions. Define (fi,F) ~ (fi x N x R,X x B(N) x B(R)),P ~ P x B(R), O =O x B(R),… 相似文献
12.
We extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012) [31] to the case of a bounded terminal condition and a generator with quadratic growth in the z variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman–Kac formula and a probabilistic representation for fully non-linear PDEs in this setting. 相似文献
13.
Krystyna Twardowska 《Acta Appl Math》1996,43(3):317-359
The aim of this paper is to give a wide introduction to approximation concepts in the theory of stochastic differential equations. The paper is principally concerned with Zong-Zakai approximations. Our aim is to fill a gap in the literature caused by the complete lack of monographs on such approximation methods for stochastic differential equations; this will be the objective of the author's forthcoming book. First, we briefly review the currently-known approximation results for finite- and infinite-dimensional equations. Then the author's results are preceded by the introduction of two new forms of correction terms in infinite dimensions appearing in the Wong-Zakai approximations. Finally, these results are divided into four parts: for stochastic delay equations, for semilinear and nonlinear stochastic equations in abstract spaces, and for the Navier-Stokes equations. We emphasize in this paper results rather than proofs. Some applications are indicated.The author's research was partially supported by KBN grant No. 2 P301 052 03. 相似文献
14.
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
15.
In this paper we study backward stochastic differential equations (BSDEs) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space K. We apply these results to prove well-posedness of a class of nonlinear parabolic differential equations on K, that generalize the Kolmogorov equation of X. Finally we formulate and solve optimal control problems for Markov jump processes, relating the value function and the optimal control law to an appropriate BSDE that also allows to construct probabilistically the unique solution to the Hamilton–Jacobi–Bellman equation and to identify it with the value function. 相似文献
16.
Norbert Christopeit 《Stochastic Processes and their Applications》1984,17(1):137-146
For a certain class of stochastic differential equations with nonlinear drift and degenerate diffusion term existence of a weak solution is shown. 相似文献
17.
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
18.
This paper concerns a class of stochastic differential equations driven by fractional Brownian motion. The existence and uniqueness of almost automorphic solutions in distribution are established provided the coefficients satisfy some suitable conditions. To illustrate the results obtained in the paper, a stochastic heat equation driven by fractional Brownian motion is considered. 1 1 The abstract section is available on the university repository site at http://math.dlut.edu.cn/info/1019/4511.htm .
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19.
A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions. 相似文献
20.
We prove an existence and uniqueness result for a general class of backward stochastic partial differential equations (SPDE) with jumps. This is a type of equations, which appear as adjoint equations in the maximum principle approach to optimal control of systems described by SPDE driven by Lévy processes. 相似文献