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A probabilistic method of solving Lobachevsky's functional equation.
- Source :
- Aequationes Mathematicae; Apr2021, Vol. 95 Issue 2, p237-243, 7p
- Publication Year :
- 2021
-
Abstract
- The aim of this paper is to give a probabilistic (martingale) characterization to the general measurable solution of the Lobachevsky functional equation. We show that finding the general solution of this equation is equivalent to establishing that a space-transformation of a Brownian Motion by a suitable function is a martingale. This method can be applied for Cauchy's, Jensen's and some other functional equations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 95
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 149694158
- Full Text :
- https://doi.org/10.1007/s00010-020-00718-1