scholarly journals On the Joint Distribution of Excursion Duration and Amplitude of a Narrow-Band Gaussian Process

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 15236-15248
Author(s):  
Mahdi Ghane ◽  
Zhen Gao ◽  
Mogens Blanke ◽  
Torgeir Moan
Keyword(s):  
Gaussian Process ◽  
Joint Distribution ◽  
Narrow Band

A Note on the Extreme Wave Load and the Associated Probability of Failure

1986 ◽  
Vol 30 (02) ◽  
pp. 123-126
Author(s):  
A. E. Mansour
Keyword(s):  
Probability Distribution ◽  
Gaussian Process ◽  
Random Process ◽  
Narrow Band ◽  
Spectral Width ◽  
Probability Of Failure ◽  
Stationary Random Process ◽  
Wave Load ◽  
Extreme Wave ◽  
Wave Statistics

Introduction and background - The probability distribution of the peak process of a stationary random process with zero mean was first determined by Rice [1]. 2 Following his basic derivation, Longuet-Higgins [2] and Cartwright and Longuet-Higgins [3] evaluated various wave statistics, first for a narrow-band Gaussian process, then extended the results for a Gaussian process of any spectral width.

BARRIER OPTIONS PRICING WITH JOINT DISTRIBUTION OF GAUSSIAN PROCESS AND ITS MAXIMUM

2017 ◽  
Vol 20 (06) ◽  
pp. 1750042
Author(s):  
PINGJIN DENG ◽  
XIUFANG LI
Keyword(s):  
Gaussian Process ◽  
Joint Distribution ◽  
Options Pricing ◽  
Time Interval ◽  
Exotic Options ◽  
Barrier Options ◽  
Rate Process ◽  
Barrier Option ◽  
Explicit Formulas ◽  
Underlying Asset

Barrier options are one of the most popular exotic options. In this contribution, we propose a performance barrier option, which is a type of barrier option defined with the [Formula: see text]th period logarithm return rate process on an underlying asset over the time interval [Formula: see text], [Formula: see text]. We show that the price of this performance barrier option is determined by the joint distribution of a Slepian process and its maximum. Furthermore, we derive a tractable formula for this joint distribution and obtain explicit formulas for the up-out-call performance option and up-out-put performance option.

Joint distribution of successive zero crossing distances for stationary Gaussian processes

1987 ◽  
Vol 24 (02) ◽  
pp. 378-385 ◽  
Author(s):  
Igor Rychlik
Keyword(s):  
Gaussian Process ◽  
Closed Form ◽  
Gaussian Processes ◽  
Joint Distribution ◽  
Closed Form Expression ◽  
Regression Curve ◽  
Form Expression ◽  
Zero Crossing ◽  
Stationary Gaussian Processes ◽  
Approximative Formula

As has been shown by de Maré, in a stationary Gaussian process the length of the successive zero-crossing intervals cannot be independent, except for the degenerate case of a pure cosine process. However, no closed-form expression of the distribution of these quantities is known at present. In this paper we present an accurate explicit approximative formula, derived by replacing the Slepian model process by its regression curve.

The Response of an Oscillator With Bilinear Hysteresis to Stationary Random Excitation

1978 ◽  
Vol 45 (4) ◽  
pp. 923-928 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
Random Process ◽  
Joint Distribution ◽  
Narrow Band ◽  
Digital Simulation ◽  
Stochastic Averaging ◽  
Random Excitation ◽  
Stationary Random Process ◽  
Simulation Results ◽  
Analytical Result ◽  
Theoretical Results

By applying the technique of stochastic averaging, a simple analytical result is obtained for the joint distribution of the displacement and velocity of a bilinear oscillator excited by a stationary random process. A comparison of theoretical results deduced from this distribution with corresponding digital simulation results shows that the theory is accurate in circumstances where the response is narrow-band in nature.

The maximum of a Gaussian process whose mean path has a maximum, with an application to the strength of bundles of fibres

1989 ◽  
Vol 21 (02) ◽  
pp. 315-333 ◽  
Author(s):  
H. E. Daniels
Keyword(s):  
Brownian Motion ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Joint Distribution ◽  
Covariance Function ◽  
Brownian Bridge ◽  
Breaking Load ◽  
Plastic Yield ◽  
Analogous Process ◽  
The Mean

Daniels and Skyrme (1985) derived the joint distribution of the maximum, and the time at which it is attained, of a Brownian path superimposed on a parabolic curve near its maximum. In the present paper the results are extended to include Gaussian processes which behave locally like Brownian motion, or a process transformable to it, near the maximum of the mean path. This enables a wider class of practical problems to be dealt with. The results are used to obtain the asymptotic distribution of breaking load and extension of a bundle of fibres which can admit random slack or plastic yield, as suggested by Phoenix and Taylor (1973). Simulations confirm the approximations reasonably well. The method requires consideration not only of a Brownian bridge but also of an analogous process with covariance function t 1(1 + t 2), .

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