共查询到20条相似文献,搜索用时 671 毫秒
1.
N.V. Lazakovich & A.L. Yablonski 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(2):135-145
The paper investigates the problem of approximation of stochastic θ-integrals and the solutions of stochastic differential equations. The complete classification of the methods of approximation of stochastic θ-integrals in the convolution algebra is proposed. It is proved that the solutions of stochastic integral equations with θ-integral can be approximated by the solutions of finite-difference equations with averaging. 相似文献
2.
Naoki Tanaka 《Israel Journal of Mathematics》2011,186(1):1-43
A viability theorem of stochastic semilinear evolution equations is discussed under a dissipative condition in terms of uniqueness
functions and a stochastic subtangential condition. Our strategy is to interpret a stochastic viability problem into a characterization
problem of evolution operators associated with stochastic semilinear evolution equations. The main theorem is a generalization
of the results due to Aubin and Da Prato in the case of stochastic differential equations in ℝ
d
. 相似文献
3.
Wei Liu 《Applied Mathematics and Optimization》2010,61(1):27-56
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with
general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation
principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and
fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle,
which is equivalent to the large deviation principle in our framework. 相似文献
4.
Wei Liu 《Journal of Evolution Equations》2009,9(4):747-770
As a Generalization to Wang (Ann Probab 35:1333–1350, 2007) where the dimension-free Harnack inequality was established for
stochastic porous media equations, this paper presents analogous results for a large class of stochastic evolution equations
with general monotone drifts. Some ergodicity, compactness and contractivity properties are established for the associated
transition semigroups. Moreover, the exponential convergence of the transition semigroups to invariant measure and the existence
of a spectral gap are also derived. As examples, the main results are applied to many concrete SPDEs such as stochastic reaction-diffusion
equations, stochastic porous media equations and the stochastic p-Laplace equation in Hilbert space. 相似文献
5.
This article is concerned with the blowup phenomenon of stochastic delayed evolution equations. We first establish the sufficient condition to ensure the existence of a unique nonnegative solution of stochastic parabolic equations. Then the problem of blow-up solutions in mean Lq-norm, q ? 1, in a finite time is considered. The main aim in this article is to investigate the effect of time delay and stochastic term. A new result shows that the stochastic delayed term can induce singularities. 相似文献
6.
The main aim of this paper is to study the stability of the stochastic functional differential equations with infinite delay.
We establish several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations
with infinite delay. By applying these results to stochastic differential equations with distributed delay, we obtain some
sufficient conditions for both pth moment and almost surely exponentially stable. Finally, some examples are presented to illustrate our theory. 相似文献
7.
p-Moment Stability of Stochastic Nonlinear Delay Systems with Impulsive Jump and Markovian Switching
Zaiming Liu 《随机分析与应用》2013,31(5):911-923
Abstract This article is concerned with the problem of p-moment stability of stochastic differential delay equations with impulsive jump and Markovian switching. In this model, the features of stochastic systems, delay systems, impulsive systems, and Markovian switching are all taken into account, which is scarce in the literature. Based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain new criteria ensuring p-moment stability of trivial solution of a class of impulsive stochastic differential delay equations with Markovian switching. 相似文献
8.
Zdzisław Brzeźniak 《Potential Analysis》1995,4(1):1-45
We study abstract stochastic evolution equations in M-type 2 Banach spaces. Applications to stochastic partial differential equations inL
p
spaces withp2 are given. For example, solutions of such equations are Hölder continuous in the space variables.The author is an Alexander von Humboldt Stiftung fellow 相似文献
9.
L. E. Shaikhet 《Journal of Mathematical Sciences》1991,53(4):457-462
Using Gateaux differentiation of the quality functional we obtain necessary conditions for optimality of a control for stochastic differential equations of hyperbolic type containing two-parameter white noise and for stochastic integral equations.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 110–116, 1987. 相似文献
10.
T. N. Kravets 《Journal of Mathematical Sciences》1991,53(1):44-48
A sequence of approximating equations is constructed for stochastic differential inclusions, and the properties of the measures corresponding to solutions of the approximating equations are studied for the class of stochastic differential inclusions.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 43–48, 1986. 相似文献
11.
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined,
especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity
solutions growing at most like o(1+|x|
p
) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient
nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply
to a larger class of solutions, namely those growing like O(1+|x|
p
) at infinity. This latter case encompasses some equations related to backward stochastic differential equations. 相似文献
12.
In this paper, we are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory’s approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the Lp-norm when the drift and diffusion coefficients are Taylor approximations. 相似文献
13.
AbstractIn this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration. 相似文献
14.
We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale. 相似文献
15.
《随机分析与应用》2013,31(5):1189-1205
Abstract In this paper, we establish the existence of solutions of a more general class of stochastic functional integral equations. The main tools here are the measure of noncompactness and the fixed point theorem of Darbo type. The results of this paper generalize the results of Rao–Tsokos [Rao, A.N.V.; Tsokos, C.P. A class of stochastic functional integral equations. Coll. Math. 1976, 35, 141–146.] and Szynal–Wedrychowicz [Szynal, D.; Wedrychowicz, S. On existence and an asymptotic behaviour of random solutions of a class of stochastic functional integral equations. Coll. Math. 1987, 51, 349–364.]. 相似文献
16.
We construct, for various classes of p-adic-valued functions, stochastic integrals with respect to the Poisson random measure. This leads to the construction of Markov processes over the field of p-adic numbers by means of stochastic differential equations. 相似文献
17.
Clément Pellegrini 《Annales Henri Poincare》2009,10(5):995-1025
Quantum Trajectories are solutions of stochastic differential equations. Such equations are called Stochastic Master Equations and describe random phenomena in the continuous measurement theory of Open Quantum System. Many recent developments deal
with the control of such models, i.e. optimization, monitoring and engineering. In this article, stochastic models with control
are mathematically and physically justified as limits of concrete discrete procedures called Quantum Repeated Measurements. In particular, this gives a rigorous justification of the Poisson and diffusion approximations in quantum measurement theory
with control. 相似文献
18.
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
19.
林清泉 《中国科学A辑(英文版)》2002,45(12):1518-1522
The notion of weak solution for stochastic differential equation with terminal conditions is introduced. By Girsanov transformation,
the equivalence of existence of weak solutions for two-type equations is established. Several sufficient conditions for the
existence of the weak solutions for stochastic differential equation with terminal conditions are obtained, and the solution
existence condition for this type of equations is relaxed. Finally, an example is given to show that the result is an essential
extension of the one under Lipschitz condition ong with respect to (Y,Z). 相似文献
20.
Loeb space methods are used to prove existence of an optimal control for general 3D stochastic Navier–Stokes equations with multiplicative noise. The possible non-uniqueness of the solutions mean that it is necessary to utilize the notion of a non-standard approximate solution developed in the paper by N.J. Cutland and Keisler H.J. 2004, Global attractors for 3-dimensional stochastic Navier–Stokes equations, Journal of Dynamics and Differential Equations, pp. 16205–16266, for the study of attractors. 相似文献