A theoretical model for a vane with stochastic rotation. (English) Zbl 07868611
Summary: In this paper we propose the mathematical model for a vane with stochastic rotation. By backward stochastic differential equation and the Feynman-Kac formula, we obtain the representation of solution to the proposed convection-diffusion equation with symmetric initial condition through the transition probability density of stochastic differential equation. Moreover the explicit probability density function of solution with \(t = 1\) and \(x = 0\) is obtained, which shows that the distribution of \(k < 0\) is bimodal distribution with double maximum. By comparing to the experiment, it is found that the angular velocity with stochastic bidirectional is the binormal distribution with \(k < 0\), thus our model can describe the rotation of a vane with stochastic rotation very well.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic rotation; convection-diffusion equation; backward stochastic differential equation; binormal distribution; symmetric functionReferences:
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