共查询到20条相似文献,搜索用时 46 毫秒
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在积分型Lipschitz条件下,证明了一类以连续鞅为驱动的随机泛函微分方程解的存在性与唯一性. 相似文献
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该文研究了非Lipschitz条件下的倒向重随机微分方程, 给出了此类方程解的存在唯一性 定理, 推广Pardoux和Peng 1994年的结论; 同时也得到了此类方程在非Lipschitz条件下的比较定理, 推广了Shi,Gu和Liu 2005年的结果. 从而推广倒向重随机微分方程在随机控制和随机偏微分方程在 粘性解方面的应用. 相似文献
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The existence and uniqueness of the solutions to high-dimensional McKean-Vlasov stochastic differential equations with discontinuous drift coefficients and corresponding particle systems, were investigated. With the drift coefficient being piecewise Lipschitz continuous about the space variable, through Zvonkin’ s transformation, the original equation was converted into a new McKean-Vlasov stochastic differential equation with Lipschitz continuous coefficients. Therefore, the new equation has a unique solution. Moreover, the existence and Lipschitz continuity of the inverse function were proven according to the transformation function characteristics. Finally, based on the Itô’ s formula and the inverse function characteristics, the existence and uniqueness of the solutions to the McKean-Vlasov stochastic differential equation and the corresponding particle system were obtained. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
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一类连续半鞅型随机微分方程解的随机稳定性 总被引:2,自引:0,他引:2
本文利用Lyapunov函数方法,讨论了时齐Doleans-Dader-Protter方程dX_t=σ(X_t)dM_t=b(X_t)dA_t+((M_t)为连续局部平方可积鞅;(A_t)为连续有限变差过程)平凡解的随机稳定性。本文建立了随机稳定性的判定定理并给出了相应的Lyapunov函数的一种具体形式。 相似文献
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大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul... 相似文献
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RELATIONS BETWEEN SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SEMIMARTINGALE WITH NON-LIPSCHITZ COEFFICIENTS 总被引:1,自引:0,他引:1
Weiyin Fei School of Math. Physics Anhui University of Technology Science Wuhu Anhui 《Annals of Differential Equations》2010,(1):16-23
In this paper, a class of stochastic differential equations (SDEs) driven by semi-martingale with non-Lipschitz coefficients is studied. We investigate the dependence of solutions to SDEs on the initial value. To obtain a continuous version, we impose the conditions on the local characteristic of semimartingale. In this case, it gives rise to a flow of homeomorphisms if the local characteristic is compactly supported. 相似文献
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Ren Yong~ 《Annals of Differential Equations》2007,23(3):319-331
In this paper,we obtain some results on the existence and uniqueness of solutions to stochastic forest evolution system under non-Lipschitz condition, with Lipschitz condition being considered as a special case.We develop our theory by investigating convergence of sequence of stochastic process defined by successive approximations in the general functional setting.The major tools we used are Bihari inequality and Davis inequality. 相似文献
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本文讨论Hilert空间中非线性随机微分-积分方程解的存在性,唯一性,在我们所 一组条件下,得到了解的局部存在唯一性的结果。 相似文献
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Xiaogang Liu 《Annals of Differential Equations》2014,(2):157-165
A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations. 相似文献
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A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients
The purpose of this paper is to study some properties of solutions to one-dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth and non-Lipschitz conditions on the coefficients. Taking inspiration from [K. Bahlali, E.H. Essaky, M. Hassani, and E. Pardoux Existence, uniqueness and stability of backward stochastic differential equation with locally monotone coefficient, C.R.A.S. Paris. 335(9) (2002), pp. 757–762; K. Bahlali, E. H. Essaky, and H. Hassani, Multidimensional BSDEs with super-linear growth coefficients: Application to degenerate systems of semilinear PDEs, C. R. Acad. Sci. Paris, Ser. I. 348 (2010), pp. 677-682; K. Bahlali, E. H. Essaky, and H. Hassani, p-Integrable solutions to multidimensional BSDEs and degenerate systems of PDEs with logarithmic nonlinearities, (2010). Available at arXiv:1007.2388v1 [math.PR]], we introduce a new local condition which ensures the pathwise uniqueness, as well as the non-contact property. We moreover show that the solution produces a stochastic flow of continuous maps and satisfies a large deviations principle of Freidlin–Wentzell type. Our conditions on the coefficients go beyond the existing ones in the literature. For instance, the coefficients are not assumed uniformly continuous and therefore cannot satisfy the classical Osgood condition. The drift coefficient could not be locally monotone and the diffusion is neither locally Lipschitz nor uniformly elliptic. Our conditions on the coefficients are, in some sense, near the best possible. Our results are sharp and mainly based on Gronwall lemma and the localization of the time parameter in concatenated intervals. 相似文献
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一类与半鞅有关的推广型脉冲控制(II) 总被引:1,自引:0,他引:1
本文在(Ⅰ)中建立了一类推广型的脉冲控制模型,证明了相应的变分方程解的存在性.本篇首先对(Ⅰ)中的结论进行了强化,进而证明了新模型最佳控制的存在性.分析表明,新模型的最佳控制呈四种形态,这与以前类似模型最佳控制只呈一种形态已有较大差异.本篇的分析方法基本上是新的. 相似文献
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管平 《数学物理学报(B辑英文版)》1998,(3)
1IntroductionLetfibeaboundeddomaininRN,yi=yi(x,f),u=u(x,t)denotethepotentialandtemperatureillsidefi,respectively.Thetherndstorproblem,whichdescribetheheatinaconductorbyanelectricalcurrent,callbestatedasfollows:wherenistheoutwardnormaltooff,andodeDistheunionofisolatedcontactpartsofthedevice,odeDnomeN=0,odeDUomeN=offandmeasoflD>0'Thesystenl(1.1),(1.2)witllDiricllletboundaryvalueorNellmannboundaryvaluehasbeenillvestigatedbyseveral..th.,s[1]--[41.G.YuallalldZ.Liu[5]provedtheexistenceanduniqu… 相似文献
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EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS 总被引:1,自引:0,他引:1
In this paper, we study a boundary value problem of nonlinear fractional differential equations of order q (1 < q ≤ 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2. 相似文献
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The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers. 相似文献