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Approximation of First Exit Times of Diffusions and Approximate Solution of Parabolic Equations

โœ Scribed by Eckhard Platen

Publisher
John Wiley and Sons
Year
1983
Tongue
English
Weight
728 KB
Volume
111
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

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 speedof convergence is estimated wit,h 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.

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In this paper, we introduce "approximate solutions" to solve the following problem: given a polynomial F (x, y) over Q, where x represents an n-tuple of variables, can we find all the polynomials G(x) such that F (x, G(x)) is identically equal to a constant c in Q? We have the following: let F (x, y