共查询到20条相似文献,搜索用时 15 毫秒
1.
Wolfgang Hackenbroch 《Archiv der Mathematik》2009,92(5):485-492
In a Hilbert space context, we propose a rather general notion of “random operators” which allows for taking stochastic limits.
After establishing a connection with measurable fields of closed operators, we may speak of a spectral theory for symmetric
random operators.
Received: 18 December 2008 相似文献
2.
Yûichirô Kakihara 《Journal of multivariate analysis》1985,16(1):140-156
Let H be a Hilbert space and B(H) be the algebra of all bounded linear operators on H. Normal Hilbert B(H)-module valued processes are studied over a locally compact abelian group as models for infinite variate or Hilbert space valued stochastic processes. Harmonizability of Rozanov type and V-boundedness are defined for such processes. It is shown that a process is harmonizable if and only if it is V-bounded and continuous. A necessary and sufficient condition is given for a process to have a stationary dilation. 相似文献
3.
V. S. Korolyuk 《Ukrainian Mathematical Journal》2005,57(9):1442-1465
We propose a system approach to the asymptotic analysis of stochastic systems in the scheme of series with averaging and diffusion
approximation. Stochastic systems are defined by Markov processes with locally independent increments in a Euclidean space
with random switchings that are described by jump Markov and semi-Markov processes. We use the asymptotic analysis of Markov
and semi-Markov random evolutions. We construct the diffusion approximation using the asymptotic decomposition of generating
operators and solutions of problems of singular perturbation for reducibly inverse operators.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1235–1252, September, 2005. 相似文献
4.
《Stochastic Processes and their Applications》2020,130(1):366-393
In this paper, we consider stationarity of a class of second-order stochastic evolution equations with memory, driven by Wiener processes or Lévy jump processes, in Hilbert spaces. The strategy is to formulate by reduction some first-order systems in connection with the stochastic equations under investigation. We develop asymptotic behavior of dissipative second-order equations and then apply them to time delay systems through Gearhart–Prüss–Greiner’s theorem. The stationary distribution of the system under consideration is the projection on the first coordinate of the corresponding stationary results of a lift-up stochastic system without delay on some product Hilbert space. Last, two examples of stochastic damped wave equations with memory are presented to illustrate our theory. 相似文献
5.
Kai Liu 《Potential Analysis》2010,33(3):291-312
A class of Langevin equations driven by Lévy processes with time delays are considered. Sufficient conditions are established
to find a unique stationary solution of functional stochastic systems studied. The concept of operator self-decomposability,
closely related to the stationary solutions, is generalized to retarded Ornstein–Uhlenbeck processes so as that useful conditions
under which random variables with self-decomposability are embedded into a stationary retarded Langevin equations are found. 相似文献
6.
Agnès Coquio 《Probability Theory and Related Fields》2000,118(3):349-364
In quantum stochastic calculus on the symmetric Fock space over L 2(ℝ+), adapted processes of operators are integrated with respect to creation, annihilation and number processes. The main property which allows this integration is that the increments of integrators between s and t act only on Fock space over L 2([s, t]). In this article, we prove that there are no other process of closable operators on coherent vectors with this property. Thus the only possible integrators in quantum stochastic calculus are the creation, annihilation and number processes. 相似文献
7.
Summary. By coupling two arbitrary riemannian connections Γ and Γ˜ on a riemannian manifold M, we perform the stochastic calculus of ɛ-variation on the path space P(M) of the manifold M. The method uses direct calculations on Ito’s stochastic differential equations. In this context, we obtain intertwinning
formulas with the Ito map for first order operators on the path space P(M) of M. By a judicious choice of the second connection Γ˜ in terms of the connection Γ, we can prolongate the intertwinning formulas to second order differential operators. Thus, we obtain expressions of heat
operators on the path space P(M) of a riemannian manifold M endowed with an arbitrary connection. The integration by parts of the laplacians on P(M) leads us to the notion of dilatation vector field on the path space.
Received: 18 April 1995 / In revised form: 18 March 1996 相似文献
8.
Salim Lardjane 《Statistical Inference for Stochastic Processes》2007,10(3):209-221
The author deals with nonparametric density estimation for stochastic processes which satisfy the L
∞-approximability property. He considers a Parzen–Rosenblatt estimator of the density for general stationary L
∞-approximable processes. He states conditions under which it is consistent and investigates its rate of convergence. Finally,
he applies his results to general nonmixing linear processes and nonmixing nonlinear autoregressive processes. 相似文献
9.
This article continues the study of Liu [Statist. Probab. Lett. 78(2008): 1775–1783; Stoch. Anal. Appl. 29(2011): 799–823] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated stochastic equations have unbounded operators acting on the point or distributed delayed terms, while the operator acting on the instantaneous term generates a strongly continuous semigroup. We present conditions on the delay systems to obtain a unique stationary solution by combining spectrum analysis of unbounded operators and stochastic calculus. A few instructive cases are analyzed in detail to clarify the underlying complexity in the study of systems with unbounded delayed operators. 相似文献
10.
E. O. Ayoola 《Acta Appl Math》2001,67(1):19-58
Several one-step schemes for computing weak solutions of Lipschitzian quantum stochastic differential equations (QSDE) driven by certain operator-valued stochastic processes associated with creation, annihilation and gauge operators of quantum field theory are introduced and studied. This is accomplished within the framework of the Hudson–Parthasarathy formulation of quantum stochastic calculus and subject to the matrix elements of solution being sufficiently differentiable. Results concerning convergence of these schemes in the topology of the locally convex space of solution are presented. It is shown that the Euler–Maruyama scheme,with respect to weak convergence criteria for Itô stochastic differential equation is a special case of Euler schemes in this framework. Numerical examples are given. 相似文献
11.
Ole E. Barndorff-Nielsen Makoto Maejima Ken-iti Sato 《Journal of Theoretical Probability》2006,19(2):411-446
General results concerning infinite divisibility, selfdecomposability, and the class L
m
property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein–Uhlenbeck type are studied in relation to these concepts. Further, time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given. 相似文献
12.
E.O. Ayoola 《随机分析与应用》2013,31(4):525-554
Multistep schemes for computing weak solutions of Lipschitzian quantum stochastic differential equations (QSDE) driven by certain operator-valued stochastic processes associated with the basic field operators of quantum field theory are introduced and studied. This is accomplished within the framework of the Hudson–Parthasarathy formulation of quantum stochastic calculus and subject to matrix element of solution being sufficiently differentiable. Results concerning convergence of explicit schemes of class A in the topology of the locally convex space of solution are presented.Numerical examples are given. 相似文献
13.
This paper examines the restrictions that may be put on joint distributions of two or more stationary stochastic processes,
and still attainđ-đ, or approach it. 相似文献
14.
CaiShiWANG ZhiYuanHUANG 《数学学报(英文版)》2004,20(6):999-1008
A family of closed snbalgebras, indexed by R(the set of real numbers), of the Wick algebra is constructed. Fundamental properties of tile family are shown including the increasing property and the right-continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators. 相似文献
15.
A notion of semi-selfsimilarity of R
d
-valued stochastic processes is introduced as a natural extension of the selfsimilarity. Several topics on semi-selfsimilar processes are studied: the existence of the exponent for semi-selfsimilar processes; characterization of semi-selfsimilar processes as scaling limits; relationship between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, and examples; construction of semi-selfsimilar processes with stationary increments; and extension of the Lamperti transformation. Semi-stable processes where all joint distributions are multivariate semi-stable are also discussed in connection with semi-selfsimilar processes. A wide-sense semi-selfsimilarity is defined and shown to be reducible to semi-selfsimilarity. 相似文献
16.
Existence, positivity and contractivity for quantum stochastic flows with infinite dimensional noise
Quantum stochastic differential equations of the form
govern stochastic flows on a C
*-algebra ?. We analyse this class of equation in which the matrix of fundamental quantum stochastic integrators Λ is infinite
dimensional, and the coefficient matrix θ consists of bounded linear operators on ?. Weak and strong forms of solution are
distinguished, and a range of regularity conditions on the mapping matrix θ are considered, for investigating existence and
uniqueness of solutions. Necessary and sufficient conditions on θ are determined, for any sufficiently regular weak solution
k to be completely positive. The further conditions on θ for k to also be a contraction process are found; and when ? is a von Neumann algebra and the components of θ are normal, these
in turn imply sufficient regularity for the equation to have a strong solution. Weakly multiplicative and *-homomorphic solutions and their generators are also investigated. We then consider the right and left Hudson-Parthasarathy
equations:
in which F is a matrix of bounded Hilbert space operators. Their solutions are interchanged by a time reversal operation on processes.
The analysis of quantum stochastic flows is applied to obtain characterisations of the generators F of contraction, isometry and coisometry processes. In particular weak solutions that are contraction processes are shown
to have bounded generators, and to be necessarily strong solutions.
Received: 3 November 1998 / Published online: 30 March 2000 相似文献
17.
Vector-valued, asymptotically stationary stochastic processes on -compact locally compact abelian groups are studied. For such processes, we introduce a stationary spectral measure and show that it is discrete if and only if the asymptotically stationary covariance function is almost periodic. Using an almost periodic Fourier transform we recover the discrete part of the spectral measure and construct a natural, consistent estimator for the latter from samples of the process. 相似文献
18.
I. N. Sinitsyn 《Computational Mathematics and Modeling》1998,9(2):167-175
The article studies stochastic processes defined by Ito stochastic differential equations with Wiener white noise. Methods
are considered that find exact expressions for finite-dimensional densities of random stationary and nonstationary (in the
narrow sense) processes based on construction of integral invariants of specially chosen systems of ordinary differential
equations.
Translated from Algoritmy Upravleniya i Identifikatsii, pp. 129–140, 1997. 相似文献
19.
Ely Merzbach 《Acta Appl Math》1988,12(1):79-101
In this survey paper, two-parameter point processes are studied in connection with martingale theory and with respect to the partial-order induced by the Cartesian coordinates of the plane. Point processes are characterized by jump stopping times and by their two-parameter compensators. Properties of the doubly stochastic Poisson process, such as predictability, are discussed. A definition for the Palm measure of a two-parameter stationary point process is proposed. 相似文献
20.
In this work, we shall consider stationary (mild) solutions for a class of retarded functional linear differential equations with additive noise in Hilbert spaces. We first introduce a family of Green operators for the stochastic systems and establish stability results which will play an important role in the investigation of stationary solutions. A criterion imposed on the Green operators is presented to identify a unique stationary solution for the systems considered. Under strong quasi-Feller property, it is shown that this criterion is a sufficient and necessary condition to guarantee a unique stationary solution, based on a method having its origins in optimal control theory. 相似文献