Search results for "First Passage"
showing 8 items of 8 documents
On reliability of systems with moving material subjected to fracture and instability
2015
Abstract The reliability of systems with moving cracked elastic and isotropic material is considered. The material is modeled as a moving plate which continually has a crack on the edge. The plate is subjected to homogeneous tension acting in the traveling direction and the tension varies temporally around a constant value, the set tension. The tension and the length of the crack are modeled by an Ornstein–Uhlenbeck process and an exponential Ornstein–Uhlenbeck process, respectively. Failure is regarded as the state at which the plate becomes unstable or fractures (or both) and a lower bound for the reliability of the system is derived. Considering reliability of the system leads to first p…
Reliability analysis of processes with moving cracked material
2015
Abstract The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: (i) tension is constant with respect to time, and (ii) tension varies temporally according to an Ornstein–Uhlenbeck process. Cracks of random length are assumed to occur in the material according to a stochastic counting process. For a general counting process, a representation of the nonfracture probability of the system is obtained that exploits condi…
First-passage problem for nonlinear systems under Lévy white noise through path integral method
2016
In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
2015
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements
2016
In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to …
Diffusive behavior and the modeling of characteristic times in limit order executions
2007
We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays asymptotically as a power law, but that of FPT has significantly fatter tails than that of TTF. Thus a simple first passage time model cannot account for the observed TTF of limit orders. We propose that the origin of this difference is the presence of cancellations. We outline a simple model, which assumes that prices are characterized by the empirically observed distribution …
Understanding the determinants of volatility clustering in terms of stationary Markovian processes
2016
Abstract Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ − β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock’s volatility is a linear function of the average correlation of such stock’s volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still kee…
Stochastic fracture analysis of systems with moving material
2015
This paper considers the probability of fracture in a system in which a material travels supported by rollers. The moving material is subjected to longitudinal tension for which deterministic and stochastic models are studied. In the stochastic model, the tension is described by a multi-dimensional Ornstein-Uhlenbeck process. The material is assumed to have initial cracks perpendicular to the travelling direction, and a stochastic counting process describes the occurrence of cracks in the longitudinal direction of the material. The material is modelled as isotropic and elastic, and LEFM is applied. For a general counting process, when there is no fluctuation in tension, the reliability of t…