scholarly journals First-passage probability: a test for DNA Hamiltonian parameters

2020 ◽  
Vol 22 (46) ◽  
pp. 26901-26909
Author(s):  
Marco Zoli
Keyword(s):  
First Passage ◽  
Hamiltonian Models ◽  
Input Parameters ◽  
First Passage Probability ◽  
Hamiltonian Parameters

A method is developed to chose the set of input parameters for DNA mesoscopic Hamiltonian models.

First-passage time for a particular stationary periodic Gaussian process

1976 ◽  
Vol 13 (01) ◽  
pp. 27-38 ◽  
Author(s):  
L. A. Shepp ◽  
D. Slepian
Keyword(s):  
Gaussian Process ◽  
Infinite Series ◽  
First Passage Time ◽  
Passage Time ◽  
Numerical Calculations ◽  
Time Interval ◽  
Two Dimensional ◽  
First Passage ◽  
Gaussian Density ◽  
First Passage Probability

We find the first-passage probability that X(t) remains above a level a throughout a time interval of length T given X(0) = x 0 for the particular stationary Gaussian process X with mean zero and (sawtooth) covariance P(τ) = 1 – α | τ |, | τ | ≦ 1, with ρ(τ + 2) = ρ(τ), – ∞ < τ < ∞. The desired probability is explicitly found as an infinite series of integrals of a two-dimensional Gaussian density over sectors. Simpler expressions are found for the case a = 0 and also for the unconditioned probability that X(t) be non-negative throughout [0, T]. Results of some numerical calculations are given.

scholarly journals First passage probability assessment of stationary non-Gaussian process using the third-order polynomial transformation

2018 ◽  
Vol 22 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Yan-Gang Zhao ◽  
Long-Wen Zhang ◽  
Zhao-Hui Lu ◽  
Jun He
Keyword(s):  
Gaussian Process ◽  
Probability Assessment ◽  
Third Order ◽  
First Passage ◽  
The Third ◽  
Polynomial Transformation ◽  
Order Polynomial ◽  
First Passage Probability ◽  
Non Gaussian ◽  
First Four Moments

In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the “softening” responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and “hardening” responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process.

scholarly journals PRICING AND HEDGING BARRIER OPTIONS IN A HYPER-EXPONENTIAL ADDITIVE MODEL

2010 ◽  
Vol 13 (05) ◽  
pp. 657-681 ◽  
Author(s):  
MARC JEANNIN ◽  
MARTIJN PISTORIUS
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Fourier Transforms ◽  
Additive Model ◽  
Barrier Options ◽  
First Passage ◽  
Numerical Illustration ◽  
Piecewise Constant ◽  
Call Options ◽  
First Passage Probability

In this paper, we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an explicit matrix Wiener-Hopf factorization. Employing this result we derive explicit expressions for the Laplace-Fourier transforms of the prices and Greeks of barrier options. As a numerical illustration, the prices and Greeks of down-and-in digital and down-and-in call options are calculated for a set of parameters obtained by a simultaneous calibration to Stoxx50E call options across strikes and four different maturities. By comparing the results with Monte-Carlo simulations, we show that the method is fast, accurate, and stable.

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