Search results for "stochastic"
showing 10 items of 1018 documents
An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves
2010
Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we pr…
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Modal analysis for random response of MDOF systems
1990
The usefulness of the mode-superposition method of multidegrees of freedom systems excited by stochastic vector processes is here presented. The differential equations of moments of every order are written in compact form by means of the Kronecker algebra; then the method for integration of these equations is presented for both classically and non-classically damped systems, showing that the fundamental operator available for evaluating the response in the deterministic analysis is also useful for evaluating the response in the stochastic analysis.
Simultaneous optimization of harvest schedule and measurement strategy
2013
In many recent studies, the value of forest inventory information in the harvest scheduling has been examined. Usually only the profitability of measuring simultaneously all the stands in the area is examined. Yet, it may be more profitable to concentrate the measurement efforts to some subset of them. In this paper, the authors demonstrate that stochastic optimization can be used for defining the optimal measurement strategy simultaneously with the harvest decisions. The results show that without end-inventory constraints, it was most profitable to measure the stands that were just below the medium age. Measuring the oldest stands was not profitable at all. It turned out to be profitable t…
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Ensemble strategies in Compact Differential Evolution
2011
Differential Evolution is a population based stochastic algorithm with less number of parameters to tune. However, the performance of DE is sensitive to the mutation and crossover strategies and their associated parameters. To obtain optimal performance, DE requires time consuming trial and error parameter tuning. To overcome the computationally expensive parameter tuning different adaptive/self-adaptive techniques have been proposed. Recently the idea of ensemble strategies in DE has been proposed and favorably compared with some of the state-of-the-art self-adaptive techniques. Compact Differential Evolution (cDE) is modified version of DE algorithm which can be effectively used to solve …
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…
LOCAL CONTROL OF SOUND IN STOCHASTIC DOMAINS BASED ON FINITE ELEMENT MODELS
2011
A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the finite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pressure field in the silent region are given by the solution of a quadratic optimization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a mod…