共查询到20条相似文献,搜索用时 0 毫秒
1.
H. Schurz 《Journal of Mathematical Analysis and Applications》2007,332(1):334-345
Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systems
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This paper deals with a class of anticipated backward stochastic differential equations. We extend results of Peng and Yang (2009) to the case in which the generator satisfies non-Lipschitz condition. The existence and uniqueness of solutions for anticipated backward stochastic differential equations as well as a comparison theorem are obtained. The existence and uniqueness of Lp(p>2) solutions for anticipated backward stochastic differential equations are also studied. 相似文献
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Seiichiro Kusuoka 《Journal of Functional Analysis》2010,258(3):758-784
I considered if solutions of stochastic differential equations have their density or not when the coefficients are not Lipschitz continuous. However, when stochastic differential equations whose coefficients are not Lipschitz continuous, the solutions would not belong to Sobolev space in general. So, I prepared the class Vh which is larger than Sobolev space, and considered the relation between absolute continuity of random variables and the class Vh. The relation is associated to a theorem of N. Bouleau and F. Hirsch. Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh. 相似文献
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On Wiener-Poisson type multivalued stochastic differential equations with non-Lipschitz coefficients
Jing Wu 《数学学报(英文版)》2013,29(4):675-690
In this paper, we prove local uniqueness for multivalued stochastic differential equations with Poisson jumps. Then existence and uniqueness of global solutions is obtained under the conditions that the coefficients satisfy locally Lipschitz continuity and one-sided linear growth of b. Moreover, we also prove the Markov property of the solution and the existence of invariant measures for the corresponding transition semigroup. 相似文献
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We introduce the concepts of Poisson square-mean almost automorphy and almost automorphy in distribution. Under suitable conditions on the coefficients, we establish the existence of solutions which are almost automorphic in distribution for some semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solutions. Finally, to illustrate the theoretical results obtained in this paper, we give several examples. 相似文献
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In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter , and a discontinuous drift. The proof of this result is based on the Girsanov theorem for the fractional Brownian motion. 相似文献
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Zhun Gou Ming-hui Wang 《Stochastics An International Journal of Probability and Stochastic Processes》2020,92(4):533-551
In this paper, the existence and pathwise uniqueness of strong solutions for jump-type stochastic differential equations are investigated under non-Lipschitz conditions. A sufficient condition is obtained for ensuring the non-confluent property of strong solutions of jump-type stochastic differential equations. Moreover, some examples are given to illustrate our results. 相似文献
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The standard existence and uniqueness theorem for stochastic differential equations requires Lipschitz condition of the coefficients. In this paper, we extend these results to the case in which the coefficients are not required to be Lipschitz continuous, instead they only satisfy a ‘weak’ type of Lipschitz condition. 相似文献
10.
《Stochastic Processes and their Applications》2014,124(5):1974-2002
In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications our main results are applied to various types of SPDE such as stochastic reaction–diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier–Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE. 相似文献
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Alka Chadha Swaroop Nandan Bora 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(5):663-681
The paper is mainly concerned with a class of neutral stochastic fractional integro-differential equation with Poisson jumps. First, the existence and uniqueness for mild solution of an impulsive stochastic system driven by Poisson jumps is established by using the Banach fixed point theorem and resolvent operator. The exponential stability in the pth moment for mild solution to neutral stochastic fractional integro-differential equations with Poisson jump is obtained by establishing an integral inequality. 相似文献
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This paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay (short for INSFDEs) at a space BC((-∞,0];Rd). Under the uniform Lipschitz condition, linear growth condition is weaken to obtain the moment estimate of the solution for INSFDEs. Furthermore, the existence, uniqueness theorem of the solution for INSFDEs is derived, and the estimate for the error between approximate solution and exact solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence, uniqueness theorem is also valid for INSFDEs on [t0,T]. Moreover, the existence, uniqueness theorem still holds on interval [t0,∞), where t0∈R is an arbitrary real number. 相似文献
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Abdelhadi Es-Sarhir 《Journal of Functional Analysis》2010,259(5):1248-1272
We study regularity properties for invariant measures of semilinear diffusions in a separable Hilbert space. Based on a pathwise estimate for the underlying stochastic convolution, we prove a priori estimates on such invariant measures. As an application, we combine such estimates with a new technique to prove the L1-uniqueness of the induced Kolmogorov operator, defined on a space of cylindrical functions. Finally, examples of stochastic Burgers equations and thin-film growth models are given to illustrate our abstract result. 相似文献
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This paper considers a class of nonlocal stochastic differential equations with time-varying delay whose coefficients are dependent on the pth moment. By applying the fixed point theorem, the existence and uniqueness of the solution of nonlocal stochastic differential delay equations is studied. Also, a class of moment estimates of solutions is considered. The results are a generalization and continuation of the recent results on this issue. An example is provided to illustrate the effectiveness of our results. 相似文献
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Paul H. Bezandry 《Applicable analysis》2013,92(7):819-827
The article introduces and studies the concept of p-mean almost periodicity for stochastic processes. Our abstract results are, subsequently, applied to studying the existence of square-mean almost periodic solutions to some semilinear stochastic equations. 相似文献
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The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence-uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence-uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results. 相似文献
17.
Yong Ren Shiping Lu Ningmao Xia 《Journal of Computational and Applied Mathematics》2008,220(1-2):364-372
In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd) which denotes the family of bounded continuous Rd-value functions defined on (-∞,0] with norm under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation. 相似文献
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This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function. 相似文献
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In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz coefficients. 相似文献
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The paper deals with the pathwise uniqueness of solutions to one-dimensional time homogeneous stochastic differential equations with a diffusion coefficient σ satisfying the local time condition and measurable drift term b. We show that if the functions σ and b satisfy a non-degeneracy condition and fundamental solution to considered equation is unique in law, then pathwise uniqueness of solutions holds. Our result is in some sense negative, more precisely we give an example of an equation with Holder continuous diffusion coefficient and nondegenerate drift for which a fundamental solution is not unique in law and pathwise uniqueness of solutions does not hold. 相似文献