Stochastic analysis Research Papers - Academia.edu (original) (raw)

In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the... more

In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao [14], Khaledi and Shaked [13], Sadegh [17], Gurler and Bairamov [7] and Navarro, Balakrishnan, and Samaniego [16]. Applications in the proportional hazard rates model are presented as well.

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution... more

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic... more

Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic analysis is performed using the First-Order Reliability Method (FORM-method 2) and the Second-Order Reliability Method (SORM). The basic random variables include laminae stiffness properties and material density, as well as the randomness in ply orientation angles. Modeling of the composite behavior utilizes a nine-noded isoparametric Lagrangian element based on the third-order shear deformation theory. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using comparisons with results of Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of composite plates, when compared to the slower Monte Carlo simulation techniques.

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution... more

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

Nowadays, interest in generating electricity using decentralized generators of relatively small scale ('distributed generation', DG) is increasing. This work deals with the impact of implementing DG on the transmission system... more

Nowadays, interest in generating electricity using decentralized generators of relatively small scale ('distributed generation', DG) is increasing. This work deals with the impact of implementing DG on the transmission system transient stability, with the emphasis on a potential transition from a 'vertical power system' to a 'horizontal power system. A problem in power systems is maintaining synchronous operation of all (centralized) synchronous machines. This stability problem associated is called rotor angle stability. In this work, the impact of the DG implementation on this is investigated. The impact of DG levels on the system transient stability when the increasing DG level is followed by a reduction of centralized generators in service resulting in a 'vertical to horizontal' transformation of the power system is also investigated. Furthermore, a stochastic analysis is used to study the transient stability of the power systems. The results show that...

We derive random implicit representations for the solutions of the classical Navier—Stokes equations for an incompressible viscous fluid. This program is carried out for Riemannian manifolds (without boundary) which are isometrically... more

We derive random implicit representations for the solutions of the classical Navier—Stokes equations for an incompressible viscous fluid. This program is carried out for Riemannian manifolds (without boundary) which are isometrically embedded in a Euclidean space (spheres, tori, n, etc.). Our results appear as an extension to smooth manifolds of the random vortex method of computational fluid dynamics. We derive these representations from gauge-theoretical considerations and the Ito formula for differential forms of stochastic analysis.

We use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, satisfy a natural... more

We use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, satisfy a natural critical action principle similar to the one encountered in classical mechanics. Several features and examples in relation with the solution semimartingales of these equations are presented.

In this paper, the approximate controllability of impulsive linear fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. By using the Banach fixed point theorems, stochastic analysis, fuzzy process... more

In this paper, the approximate controllability of impulsive linear fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. By using the Banach fixed point theorems, stochastic analysis, fuzzy process and fuzzy solution, some sufficient conditions are given for the approximate controllability of the system. KEY WORDS Approximate controllability, impulsive linear fuzzy stochastic differential equations, fuzzy solution, fixed point theorems, nonlocal conditions.

Effectiveness of the Universal Pension Fund Societies which are managers of the Open Pension Funds are usually evaluated by comparing the different types of financial and economic indicators; comparing the value of the investment... more

Effectiveness of the Universal Pension Fund Societies which are managers of the Open Pension Funds are usually evaluated by comparing the
different types of financial and economic indicators; comparing the value
of the investment portfolio or by changing the value of the units. These
comparisons are mostly incomplete and also there are no multi-dimensional
comparisons. The article attempt to check the effectiveness of the Universal
Pension Fund Societies using two alternative methods of frontier analysis: the
parametric Stochastic Frontier Analysis (SFA) and nonparametric Data
Envelopment Analysis (DEA). Two alternative models were used for each of
the methods. Comparison of the effectiveness of Universal Pension Fund
Societies from both, the customer's and the company's perspective were also
done in the article. The research have shown that there are differences in the
effectiveness of the Universal Pension Fund Societies based on value
of portfolio as well as the perspective used in the measurement.

This paper is devoted to prove, in a nonclassical function space, the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes... more

This paper is devoted to prove, in a nonclassical function space, the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution... more

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a chi2\chi^2chi2-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at ca.ca.ca. a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of kappa\kappakappa points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter, extensive efforts have been made, but... more

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter, extensive efforts have been made, but with limited success, to generalize the Zwanzig–Mori projection formalism, originally developed for Hamiltonian systems close to thermodynamic equilibrium, to general non-Hamiltonian systems lacking detailed balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent discovery that a non-Hamiltonian system defined by a set of stochastic differential
equations can be mapped to a Hamiltonian system, we develop such general projection formalism. In the resulting generalized Langevin equations, a set of generalized fluctuation–dissipation relations connect the memory kernel and the random noise terms, analogous to Hamiltonian systems obeying detailed balance. Lacking of these relations restricts previous application of the generalized Langevin formalism. Result of this work may serve as the theoretical basis for further technical developments
on model reconstruction with reduced degrees of freedom. We first use an analytically solvable example to illustrate the formalism and the fluctuation–dissipation relation. Our numerical test on a chemical network with end-product inhibition further demonstrates the validity of the formalism. We suggest that the formalism can find wide applications in scientific modeling. Specifically, we discuss potential applications to biological networks. In particular, the method provides a suitable framework for gaining insights into network properties such as robustness and parameter transferability