Abstract
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. After solving the combinatorial problems, we introduce an approximation allowing to reduce these equations to a set of linear equations for a finite number of unknown functions. Imposing natural conditions, we obtain a closed system of linear equations which can be solved for a given surface. Its solutions can be used to approximate the distribution of hitting probabilities for a regular surface with compact support.
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© 2002 Springer Science+Business Media Dordrecht
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Grebenkov, D.S. (2002). Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D. In: Malyshev, V., Vershik, A. (eds) Asymptotic Combinatorics with Application to Mathematical Physics. NATO Science Series, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0575-3_10
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DOI: https://doi.org/10.1007/978-94-010-0575-3_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0793-4
Online ISBN: 978-94-010-0575-3
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