Showing papers in "Stochastic Analysis and Applications in 1992"
TL;DR: In this article, an abstract stochastic Navier-Stokes equation with multiplicative white noise is considered, and the existence and uniqueness of a solution are proved for small initial data.
Abstract: An abstract stochastic Navier-Stokes equation with multiplicative white noise is considered. 2-dimensional Navier-Stokes equations with noise depending on first order derivatives of the solution are covered by the abstract model. Existence and uniqueness of a solution is proved for small initial data, and the associated local stochastic flow is constructed
107 citations
TL;DR: In this article, a method for approximating the multiple stochastic integrals appearing in stochaslic Taylor expansions is proposed, based on a series expansion of the Brownian bridge process.
Abstract: A method for approximating the multiple stochastic integrals appearing in stochaslic Taylor expansions is proposed. It is based on a series expansion of the Brownian bridge process. Some higher order time discrete approximations for the simulation of Ito processes using these approximate multiple stochastic integrals arc also included.
86 citations
TL;DR: In this paper, a new result on stochastic convolution and an application to stocastic differential equations in Hilbert spaces is given. But this result is only applicable to stochastically convolution.
Abstract: We give a new result on stochastic convolution and an application to stocastic differential equations in Hilbert spaces
64 citations
TL;DR: In this paper, an optimal stabilizing compensator for the case of state-dependent white noise was constructed for a single-input single-output (SISO) model with state dependent white noise.
Abstract: Results concerning construction of an optimal stabilizing compensator are obtained for the case of state-dependent white noise
62 citations
56 citations
TL;DR: In this article, an approximation theorem of the Wong-Zakai type for stochastic evolution equations in a Hilbert space with the noise being the generalized derivative of the Wiener process with values in another Hilbert space was examined.
Abstract: In this paper we examine an approximation theorem of the Wong–Zakai type for stochastic evolution equations in a Hilbert space with the noise being the generalized derivative of the Wiener process with values in another Hilbert space As a consequence of the approximation of the Wiener process we get in the limit equation the Ito correction term for the infinite dimensional case The obtained result includes the case of stochastic delay equations The uniqueness and existence of solutions are guaranteed by known theorems for the mild solutions
31 citations
TL;DR: In this paper, a generalization of the projection pursuit regression algorithm (see P.Huber [4]) in Hilbert space is presented, and theorem 2.1 states the strong convergence of the generalized algorithm.
Abstract: The paper deals with a generalization of the projection pursuit regression algorithm (see P.Huber [4]) in Hilbert space. Theorem 2.1 states the strong convergence of the generalized algorithm. This result then applied to certain spaces in order to define a new density estimator and to obtain results on density approximation and estimation
26 citations
TL;DR: In this paper, the degree of this approximation is estimated by establishing some Jackson type inequalities, and the degree is then estimated by a wavelet operator that preserves mone tonicity and transforms continuous probability distributions into probability distributions.
Abstract: Continuous functions are approximated by wavelet operators. These preserve mone tonicity and transform continuous probability distribution functions into probability distribution functions. The degree of this approximation is estimated by establishing some Jackson type inequalities
25 citations
TL;DR: Bilinear stochastic evolution equations in Hilbert spaces with unbounded operators are studied by means of the semigroup approach in this paper, and general abstract results of regularity and well posedness are proved and applied to several more concrete problems, like classical variational equations, parabolic equations in non-variational form, non-homogeneous boundary value problems and feedback boundary control problems, and finally some equations which are not of parabolic type.
Abstract: Bilinear stochastic evolution equations in Hilbert spaces with unbounded operators are studied by means of the semigroup approach. [BGeneral abstract results of regularity and well posedness are proved and applied to several more concrete problems, like classical variational equations, parabolic equations in non-variational form, non-homogeneous boundary value problems and feedback boundary control problems, and finally some equations which are not of parabolic type
13 citations
TL;DR: In this article, the stability of viscoelastic bars compressed by stochastic forces at infinite time interval is investigated and the problem of the bar buckling is considered in dynamic statement.
Abstract: This paper is devoted to the investigation of stability of viscoelsstic bars compressed by stochastic forces at infinite time interval, The problem of the bar buckling is considered in dynamic statement. Some sufficient conditions of mean square stability of viscoelastic bars are derived for arbitrary relaxation measure and different types of the end fixing
13 citations
TL;DR: In this paper, the authors consider the chaotic behavior of solutions of semi-inear stochastic evolution equations and prove the existence of the largest attractor of probability measures to which the Markovian transition probabilistic convergence converges.
Abstract: We consider the chaotic behavior of solutions of semi1inear stochastic evolution equations.We prove the existence of the largest attractor of probability measures to which the Markovian transition probabi1ity converges
TL;DR: In this paper, a semi-regenerative approach was used to obtain the invariant probability measure and the transient distribution for the embedded Markov chain in a bulk single server queue.
Abstract: This article analyzes some stochastic processes that arise in a bulk single server queue with continuously operating server, state dependent compound Poisson input flow and general state dependent service process. The authors treat the queueing process as a semi–regenerative process and obtain the invariant probability measure and the transient distribution for the embedded Markov chain. The stationary probability measure for the queueing process with continuous time parameter is found by using semi-regenerative techniques. The authors also study the input and output processes and establish ergodic theorems for some functionals of these processes. The results are obtained in terms of the invariant probability measure for the embedded process and the stationary measure for the queueing process with continuous time parameter
TL;DR: In this paper, the degree of this approximation is estimated by establishing some Jackson type inequalities, and the degree is then estimated by using a wavelet operator to transform continuous probability distributions into probability distribution functions at the same time preserving certain convexity conditions.
Abstract: Continuous functions are approximated by wavelet operators. These preserve convexity and r-convexity and transform continuous probability distribution functions into probability distribution functions at the same time preserving certain convexity conditions. The degree of this approximation is estimated by establishing some Jackson type inequalities
TL;DR: In this paper, the main objective is to develop asymptotic theory for a computable finite dimensional approximation scheme, and a sequence of monotone projection operators is employed in the recursive algorithm.
Abstract: Stochastic approximation in a Hilbert space is considered. The main objective is to develop asymptotic theory for a computable finite dimensional approximation scheme. Nonlinear operators are treated, and a sequence of monotone projection operators is employed in the recursive algorithm. Under suitable conditions, convergence with respect to the weak topology is obtained
TL;DR: In this article, the Hilbert space valued second order stochastic processes over the real line are considered and various hmonizabilities and V-boundedness are introduced and their interrelations are obtained as well as heir integral representations.
Abstract: Hilbert space valued second order stochastic processes over the real line are considered. Various hmonizabilities and V-boundednesses are introduced and their interrelations are obtained as well as heir integral representations. Examples are given to distinguish most of the harmonizabilities. Stationary dilations of harmonizable processes are also discussed. Finally, for some harmonizabilities, some convergence theorems for sequences of processes are obtained
TL;DR: Using a result in multiple integrals, the joint distribution function of the backward and forward recurrence times for the time dependent ordinary renewal process is derived in this article, where a similar methodology is used to find the distribution of their sums.
Abstract: Using a result in multiple integrals, the joint distribution function of the backward and forward recurrence times for the time dependent ordinary renewal process is derived. A similar methodology is used to find the distribution of their sums. The well known limiting behavior of these distributions is recovered
TL;DR: In this paper, the authors present a result on the question of existence uniqueness and regularity of solutions for a large class of nonlinear stochastic evolution equations, which is related to our work.
Abstract: In this paper we present a result on the question of existence uniqueness and regularity of solutions for a large class of nonlinear stochastic evolution equations
TL;DR: In this article, an asymptotic optimal two-stage procedure for allocating a fixed number of trials between two populations in order to estimate the difference between their means with squared error loss is presented.
Abstract: This paper provides an asymptotic optimal two stage procedure for allocating a fixed number of trials between two populations in order to estimate the difference between their means with squared error loss
TL;DR: In this paper, it was shown that the L 2 2/2 -boundedness class of Bochner's processes forms an essential subclass of generalized harmonizable random processes, in a sense of Gel'fand and Ito.
Abstract: It is shown that the L 2/2:-boundedness class (of Bochner's) forms an essential subclass of generalized harmonizable random processes, in a sense of Gel’fand and Ito A solution of the linear filtering problem for this family is presented An extension of the class in relation to Cramer–Karhunen families and the related Lp,p -bounded processes are also discussed The filtering equation to the latter classes needs several new restrictions
TL;DR: In this article, the Stratonovich-Taylor expansion of stochastic integrals has been used for numerical simulation of a special representation of differential equations and a means for checking the local errors of numerical methods.
Abstract: By a special representation of stochastic differential equations we give a notationally and computationally convenient Stratonovich–Taylor expansion of stochastic integrals. The expansion gives a prescription for numerical simulation of stochastic differential equations and a means for checking the local errors of numerical methods
TL;DR: In this article, the problem of allocating a fixed number of trials between the failure times of two independent components with unknown mean times to failure, in order to estimate with squared error loss, is addressed.
Abstract: This paper is concerned with the problem of allocating a fixed number of trials between the failure times of two independent components with unknown mean times to failure , in order to estimate with squared error loss. Introducing independent gamma priors on θ and ω, a fully sequential procedure is derived and shown to be nearly optimal. Monte Carlo results indicate that the fully sequential procedure performs much better than the best fixed allocation procedure
TL;DR: In this paper, a prophet inequality with constant ≤ 3.15 was obtained for subadditive processes, and applications to optimal stopping of sums of independent random variables were given, where the prophet inequality was shown to be equivalent to a constant.
Abstract: A prophet inequality with constant ≤ 3.15 is obtained for subadditive processes. Applications to optimal stopping of sums of independent random variables are given
TL;DR: For the d-dimensional reflecting stochastic differential equations (1) with non-smooth boundary and unbounded domain the existence of a strong solution, (weak solution) is obtained under the conditions that the coefficients are less than linear growth and they are non-Lipschitz, (and the diffusion coefficient is non-degenerate, the drift coefficient is bounded and measurable only) as discussed by the authors.
Abstract: For the d–dimensional reflecting stochastic differential equations (1) with non-smooth boundary and unbounded domain the existence of a strong solution, (weak solution) is obtained under the conditions that the coefficients are less than linear growth and they are non-Lipschitz, (and the diffusion coefficient is non-degenerate, the drift coefficient is bounded and measurable only). Moreover, the Girsanov theorem and the martingale representation theorem with respect to system (1) are also derived. Then by using the Ekeland lemma and the martingale method the existence, necessary and sufficient conditions for an optimal control and an optimal control are obtained. The results are then applied to solve an optimal control problem for a stochastic population model
TL;DR: It is shown that in the case of dynamic routing, the SQRT is an excellent solution to remedy the performance degradation caused by CP and CS schemes.
Abstract: In this paper, the congestion control in store and forward computer com-munication networks is studied, the method employed consists of a combination of a dynamic routing policy that minimizes the delay, and buffer nianagement schemes to control the flow of data. Simulation using liner programming has been carried out, under balanced and transient traffic conditions, on a simple 3–node network , the relative merits and drawbacks of each approach are discussed. Irland [2], showed that with static routing, the SQRT scheme improves the switch performance. In this paper it is shown that in the case of dynamic routing, the SQRT is an excellent solution to remedy the performance degradation caused by CP and CS schemes
TL;DR: In this article, the authors studied the limiting distribution of a mean zero and variance-one stationary Gaussian process with long-range dependence, and compared it with the known results on the limiting distributions of, and compared their results to those of the Gaussian Processes with Long-range Dependencies.
Abstract: Let {Xn, n∊Z} be a mean-zero and variance-one stationary Gaussian process with long-range dependence. Given functions G(x) h(x,y) and H(x,y), and an i.i.d. sequence {Yn, n∊Z} which is independent of {Xn } we study the limiting distribution of , and compare it with the known results on the limiting distribution of
TL;DR: In this paper, the relationship between the Ito integral and the Stratonovich integral is investigated and it is shown that the integrals coincide on a large class of complex valued processes.
Abstract: In this paper we are concerned with the relationship between the Ito and the Stratonovich integral. The purpose is to prove that the integrals coincide on a large class of complex valued processes
TL;DR: This paper focuses initially on an object recognition problem in which the characteristic features of the object are reported by remote sensors, and extends the method to a more general class of selection problems and considers several different scenarios.
Abstract: In this paper we consider the problem of selecting an object or a course of action from a set of possible alternatives. To give the paper focus, we concentrate initially on an object recognition problem in which the characteristic features of the object are reported by remote sensors. We then extend the method to a more general class of selection problems and consider several different scenarios. Information is provided by a set of knowledge system reports on a single feature, and the output from these systems is not totally explicit but provides posible values for the observed feature along with a degree of certitude.We use fuzzy sets to represent this vague information. Information from independent sources is combined using the Dempster-Shafer approach adapted to the situation in which the focal elements are fuzzy as in the recent paper by J. Yen [7]. We base our selection rule on the belief and plausibility functions generated by this approach to accessing evidence. For situations in which the informat...
TL;DR: In this article, an optimal sequential decision procedure for deciding between two composite hypotheses about the unknown failure rate of an exponential distribution, using censored data, is presented. But the procedure has two components, a stopping time and a decision function, and the main result determines the continuation region for the optimal decision procedure.
Abstract: This paper provides an optimal sequential decision procedure for deciding between two composite hypotheses about the unknown failure rate of an exponential distribution, using censored data. The procedure has two components, a stopping time and a decision function. The optimal stopping time minimizes the expected total loss due to a wrong decision plus cost of observing the process. The optimal decision function is easily characterized once a stopping time has been specified. The main result determines the continuation region for the optimal decision procedure
TL;DR: In this paper, it was shown that the stochastic integral of an operator-valued integrand with respect to a continuous local martingale in Hilbert spaces can be defined for almost every sample path via a sequence of simple progressively measurable approximations.
Abstract: It is proved that, under the usual measurability and the square-integrability conditions, the stochastic integral of an operator-valued integrand with respect to a continuous local martingale in Hilbert spaces can be defined for almost every sample path via a sequence of simple progressively measurable approximations. The result generalizes McKeanls construction of the It6 integral with respect to a one-dimensional Brownian motion
TL;DR: In this article, the convergence of a sequence of irreducible positive-recurrent Markov chains to a Markov chain ξ in terms of Fourier representation is studied.
Abstract: Convergence is studied of a sequence (nξ) of irreducible positive-recurrent Markov chains to a Markov chain ξ in term of Fourier representation. If (ζ∞,ωc) is the representative class of ξ by directed circuits c with the weights having a probabilistic interpretation in term of Sample paths,then the sum of all ωc for which the pair of states (i, j) is an arc of c is approximated by an almost surely convergent sequence of Fourier representations. When the weights have not a probabilistic interpretation then they can be explicitely given by an algorithm in term of the integral representation