Abstract
This chapter relates the first passage time (FPT) from a point to the boundary of a given domain to total population, flux, rate, mean time spent at a point, eigenvalues, and other quantities
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Notes
- 1.
It is known in partial differential equations theory in higher dimensions that at boundary points where \(\sum {_{i,j}\sigma }^{ij}{(\mbox{ $\boldsymbol{x}$})\nu }^{i}{(\mbox{ $\boldsymbol{x}$})\nu }^{j}(\mbox{ $\boldsymbol{x}$}) = 0\) , boundary conditions can be imposed only at points where \(\mbox{ $\boldsymbol{a}$}(\mbox{ $\boldsymbol{x}$}) \cdot \mbox{ $\boldsymbol{\nu }$}(\mbox{ $\boldsymbol{x}$}) < 0\) (Fichera 1960).
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Schuss, Z. (2013). The First Passage Time to a Boundary. In: Brownian Dynamics at Boundaries and Interfaces. Applied Mathematical Sciences, vol 186. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7687-0_4
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DOI: https://doi.org/10.1007/978-1-4614-7687-0_4
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