共查询到20条相似文献,搜索用时 31 毫秒
1.
Kenneth L. Kuttler 《Applicable analysis》2013,92(12):2456-2477
A method for obtaining measurable solutions to stochastic evolution equations in which there is no uniqueness for the corresponding non-stochastic equation is presented. It involves a technique based on a measurable selection theorem for set-valued functions. No assumptions are needed on the underlying probability space. An application is given to the stochastic Navier–Stokes problem in arbitrary dimensions. We also show the existence of measurable solutions to stochastic ordinary differential equations in which there is no uniqueness. A finite-dimensional generalization is given to adapted solutions in the case of a normal filtration and path uniqueness. 相似文献
2.
The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for stochastic functional equations with infinite delay. The main aim of this paper is to establish the existence-and-uniqueness theorems of global solutions for stochastic functional differential equations with infinite delay. 相似文献
3.
The fractional stochastic differential equations have wide applications in various fields of science and engineering. This paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces. Using fractional calculations, fixed point technique, stochastic analysis theory and methods adopted directly from deterministic fractional equations, new set of sufficient conditions are formulated and proved for the existence of mild solutions for the fractional impulsive stochastic differential equation with infinite delay. Further, we study the existence of solutions for fractional stochastic semilinear differential equations with nonlocal conditions. Examples are provided to illustrate the obtained theory. 相似文献
4.
An upper bound for the solutions of stochastic differential equations for which the drift satisfies a usual stability assumption is given. This bound, valid for any time, only needs to make use of explicit constants which can be obtained from the coefficients of these stochastic differential equations. The same kind of result is obtained for Lyapounov functions. 相似文献
5.
It is well known that the numerical solution of stiff stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit or semi-implicit methods with a wide variety of stability properties. However, for stiff stochastic problems in which the eigenvalues of a drift term lie near the negative real axis, such as those arising from stochastic partial differential equations, explicit methods with extended stability regions can be very effective. In the present paper our aim is to derive explicit Runge–Kutta schemes for non-commutative Stratonovich stochastic differential equations, which are of weak order two and which have large stability regions. This will be achieved by the use of a technique in Chebyshev methods for ordinary differential equations. 相似文献
6.
《Stochastic Processes and their Applications》2020,130(4):1879-1896
In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combining the technique of Lyapunov functions with Krylov’s estimate, we also establish exponential ergodicity for the unique strong solution. 相似文献
7.
We prove a convergence theorem for a family of value functions associated with
stochastic control problems whose cost functions are defined by backward stochastic
differential equations. The limit function is characterized as a viscosity solution
to a fully nonlinear partial differential equation of second order. The key
assumption we use in our approach is shown to be a necessary and sufficient assumption
for the homogenizability of the control problem. The results generalize partially
homogenization problems for Hamilton–Jacobi–Bellman equations treated recently by
Alvarez and Bardi by viscosity solution methods. In contrast to their approach, we
use mainly probabilistic arguments, and discuss a stochastic control interpretation
for the limit equation. 相似文献
8.
Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well
understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the
important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically
weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty
and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations
whose drift functions have at most polynomial growth. 相似文献
9.
Stability analysis of highly nonlinear hybrid multiple-delay stochastic differential equations
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Chen Fei Weiyin Fei Xuerong Mao Mingxuan Shen Litan Yan 《Journal of Applied Analysis & Computation》2019,9(3):1053-1070
Stability criteria for stochastic differential delay equations (SDDEs) have been studied intensively for the past few decades. However, most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability of highly nonlinear hybrid stochastic differential equations with a single delay is investigated in [Fei, Hu, Mao and Shen, Automatica, 2017], whose work, in this paper, is extended to highly nonlinear hybrid stochastic differential equations with variable multiple delays. In other words, this paper establishes the stability criteria of highly nonlinear hybrid variable multiple-delay stochastic differential equations. We also discuss an example to illustrate our results. 相似文献
10.
In this paper, we study the stability of nonlinear impulsive stochastic differential equations in terms of two measures. The concept of perturbing Lyapunov functions is introduced to discuss stability properties of solutions of nonlinear impulsive stochastic differential equations in terms of two measures. By using perturbing Lyapunov functions and comparison method, some sufficient conditions for the above stability are given. 相似文献
11.
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
12.
本文研究了带跳中立型随机泛函微分方程的p阶矩指数稳定性,通过构造Lyapunov函数,运用分析的技巧得到了p阶指数稳定的准则.同时给出了一个例子显示出我们的结果是有效的. 相似文献
13.
In this work, we investigate stochastic partial differential equations with variable delays and jumps. We derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions, and generalize the results obtained by Taniguchi [T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl. 331 (2007) 191-205] and Wan and Duan [L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. Probab. Lett. 78 (5) (2008) 490-498] to cover a class of more general stochastic partial differential equations with jumps. Finally, an illustrative example is established to demonstrate our established theory. 相似文献
14.
This paper is concerned with the pth moment exponential stability of stochastic functional differential equations with impulses. Based on average dwell-time method, Razumikhin-type technique and vector Lyapunov function, some novel stability criteria are obtained for impulsive stochastic functional differential systems. Two examples are given to demonstrate the validity of the proposed results. 相似文献
15.
Gorica Pavlovi? Svetlana Jankovi? 《Journal of Computational and Applied Mathematics》2012,236(7):1679-1690
To the best of the authors’ knowledge, there are no results based on the so-called Razumikhin technique via a general decay stability, for any type of stochastic differential equations. In the present paper, the Razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay. The obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay. Some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given. An example is presented to illustrate the usefulness of the theory. 相似文献
16.
Anna Milian 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):79-108
This paper establishes an anticipating stochastic differential equation of parabolic type for the expectation of the solution of a stochastic differential equation conditioned on complete knowledge of the path of one of its components. Conversely, it is shown that any appropriately regular solution of this stochastic p.d.e. must be given by the conditional expectation. These results generalize the connection, known as the Feynman-Kac formula, between parabolic equations and expectations of functions of a diffusion. As an application, we derive an equation for the unnormalized smoothing law of a filtering problem with observation feedback. 相似文献
17.
For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided. 相似文献
18.
We extend the Stieltjes integral to Hölder functions of two variables and prove an existence and uniqueness result for the corresponding deterministic ordinary differential equations and also for stochastic equations driven by a two-parameter fractional Brownian motion. 相似文献
19.
Huijie Qiao Jinqiao Duan 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(6):864-883
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two special cases, stationary measures are given by solutions of Fokker–Planck equations and long time limits for the distributions of system states. 相似文献
20.
Annalisa Cesaroni 《Applied Mathematics and Optimization》2006,53(1):1-29
We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular,
we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems.
This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations.
We define the appropriate concept of the Lyapunov function to study stochastic open loop stabilizability in probability and
local and global asymptotic stabilizability (or asymptotic controllability). Finally, we illustrate the theory with some examples. 相似文献