Random ideas: stochastic calculus and more

Exponential timestepping algorithms are efficient for exit-time problems because a boundary test can be performed at the end of each timestep, giving high-order convergence in numerical evaluation of mean exit times. Successive time increments are independent random variables with an exponential distribution. In the figure on the right, one realization is depicted. Exponential timesteps are jumps from one black point to the next. The values of the process at these times are generated, but not the corresponding times. |

Downloadable programs: | Timestepping with boundary test |
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Exit from Circle | Circle.c Circle2.c |

Exit from Sphere | Sphere.c |

Exit from Ellipse | Ellipse2D.c |

Exit from concave region | Hyp.c Hyp2.c |

Header file | MySignals.h |

Downloadable programs in: | C | FORTRAN90 / HPF |
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Basic timestepping | Exp01.c | Expdw01.f eeF90.in |

Timestepping with boundary test | Expb01.c | Expbdw01.f dwb.in |

Please note: On some web sites, the author list for the above paper appears differently. The correct author list, in spelling and in alphabetical order, is as above and any different versions are incorrect, and should be ignored.

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