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September 1996 On the stochastic equation L(X)=L[B(X+C)] and a property of gamma distributions
Daniel Dufresne
Bernoulli 2(3): 287-291 (September 1996). DOI: 10.3150/bj/1178291724


This paper is concerned with the stochastic equation X = B(X+C), where B, X and C are independent. This equation has appeared in a number of contexts, notably in actuarial science. An apparently new property of gamma variables (Theorem 1) leads to the derivation of a new explicit example of solution of the stochastic equation (Theorem 2), where B is the product of two independent beta variables, C is gamma and X is the product of independent beta and gamma variables. Also, a number of previously known explicit examples are seen to be direct algebraic consequences of a well-known property of gamma variables.


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Daniel Dufresne. "On the stochastic equation L(X)=L[B(X+C)] and a property of gamma distributions." Bernoulli 2 (3) 287 - 291, September 1996.


Published: September 1996
First available in Project Euclid: 4 May 2007

zbMATH: 0859.60064
MathSciNet: MR1416868
Digital Object Identifier: 10.3150/bj/1178291724

Keywords: discounted sums , gamma variables , hypergeometric functions

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability


Vol.2 • No. 3 • September 1996
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