First Passage Time of Nonlinear Diffusion Processes with Singular Boundary Behavior
| Autor: | Navaratnam Sri Namachchivaya, Leo Dostal |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
Acoustics and Ultrasonics Stochastic process Mechanical Engineering Probability (math.PR) Mathematical analysis Boundary (topology) Duffing equation 020101 civil engineering 02 engineering and technology Singular point of a curve Condensed Matter Physics 0201 civil engineering Quadrature (mathematics) Nonlinear system 020303 mechanical engineering & transports Mathematics - Analysis of PDEs 0203 mechanical engineering Mechanics of Materials FOS: Mathematics Diffusion (business) First-hitting-time model Mathematics - Probability Analysis of PDEs (math.AP) |
| Popis: | New theorems for moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary xe are formulated. This important class of one dimensional stochastic processes results among others from approximations of the energy or amplitude of second order nonlinear stochastic differential equations. Since the diffusion of a stochastic process vanishes at an entrance boundary, xe is called a singular point of the stochastic process. The theorems for the moments of the first passage times are validated based on existing analytical results. In addition, the first passage times of a forced and damped Mathieu oscillator, as well as a nonlinear stochastic differential equation, which is important for the determination of dangerous ship roll dynamics, are calculated. The proposed analytical expressions for the moments of the first passage times can be calculated very fast using standard quadrature formulas. |
| Databáze: | OpenAIRE |
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