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Approximation of First Exit Times of Diffusions and Approximate Solution of Parabolic Equations
Author(s) -
Platen Eckhard
Publication year - 1983
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19831110105
Subject(s) - mathematics , degenerate energy levels , bounded function , parabolic partial differential equation , convergence (economics) , monte carlo method , diffusion , mathematical analysis , heat equation , partial differential equation , physics , statistics , quantum mechanics , economics , thermodynamics , economic growth
In the paper the first exit time of a diffusion from a bounded region is approximated by first exit times of time discrete diffusion approximations. Their speed of convergence is estimated with respect to the maximum step size. Finally, this result is applied for the construction of approximate solutions of degenerate parabolic equations which can be used in Monte‐Carlo simulation algorithms.