共查询到20条相似文献,搜索用时 15 毫秒
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彭实戈通过倒向随机微分方程介绍了g-估价的概念.一般来说,给定一个生成元g,对应的条件g-估价系统通常不是齐次,可加或线性的,那么我们自然要问:满足什么样条件的生成元g才能使得这些性质成立,本文回答了这一问题. 相似文献
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彭实戈通过倒向随机微分方程引入了g-期望的概念.在关于g-期望的最基本的条件下,提出并证明了:半正定(半负定)二元函数基于g-期望的Jensen不等式在非空数集S上成立当且仅当生成元g在S上是超线性(次线性)的. 相似文献
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JIANG Long Department of Mathematics China University of Mining Technology Xuzhou China Institute of Mathematics Fudan University Shanghai China School of Mathematics System Sciences Shandong University Jinan China 《中国科学A辑(英文版)》2006,49(10):1353-1362
This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique. 相似文献
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Long Jiang~ 《应用数学学报(英文版)》2004,20(3):507-512
It is proved that a probability measure is dominated by g-expectation ε_μ[·] if and only if it can begenerated by Girsanov transformation via a process which is uniformly bounded by μ. 相似文献
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Long JIANG Department of Mathematics China University of Mining Technology Xuzhou Jiangsu China School of Mathematical Sciences Fudan University Shanghai China School of Mathematics System Sciences Shandong University Jinan China. 《数学年刊B辑(英文版)》2006,27(5)
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) = 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for g-expectation in [4, 7-9]. 相似文献
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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
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Sheng Jun FAN 《数学学报(英文版)》2007,23(8):1427-1434
In this paper, under the most elementary conditions on a backward stochastic differential equation (BSDE for short) introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of "process", based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved. 相似文献
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范胜君 《数学年刊A辑(中文版)》2006,(5)
在文[8]的基础上和彭实戈提出的关于g-期望的最基本的条件下,证明了g-期望关于凸(凹)函数的Jensen不等式在一般意义下成立当且仅当g是关于(y,z)的超齐次(次齐次)生成元且不依赖于y. 相似文献
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Sheng Jun Fan 《数学学报(英文版)》2009,25(10):1681-1692
Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen's inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang's results, under the same assumptions as Jiang's, we investigate the necessary and sufficient condition on g under which Jensen's inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen's inequality for BSDEs. 相似文献
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吴臻 《数学建模及其应用》2015,4(1):7-10
正倒向随机微分方程源于随机控制和金融等问题的研究,反之,方程理论的研究成果在控制、金融等领域也有着重要的应用。基于正向和倒向随机微分方程的理论成果,正倒向随机微分方程的研究在短时间内取得了长足进步。本文将从方程可解性这一角度出发,对正倒向随机微分方程目前取得的成果进行系统的总结与探讨。 相似文献
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提出并证明了一类常微分方程解的存在唯一性成立的一个充要条件,并给出了多项式形式增长函数的一列上界.最终将此结果应用到证明一类倒向随机微分方程的唯一解问题. 相似文献
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Nacira Agram 《Stochastics An International Journal of Probability and Stochastic Processes》2019,91(7):1041-1066
ABSTRACTOur purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case.
In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem.
For infinite horizon, we derive sufficient and necessary maximum principles.
As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.
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In this paper,we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t,y,z),when the terminal data is in L p spaces,for 1 < p ≤ 2. 相似文献
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Youssef Ouknine 《随机分析与应用》2013,31(4):871-888
Abstract The article is devoted to representation of weak solutions (in Sobolev sense) of degenerate parabolic partial differential equations through forward-backward stochastic differential equations. Before, we prove a weak version of a norm equivalence result. 相似文献