Geodesic
A renewal equation in a multidimensional space
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 779-785 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following renewal equation in a multidimensional space (REMS) is considered $$ f(x)=g(x)+\int_{R^n}K(x-t)\,f(t)\,dt, $$ where $K$ is the density of a distribution in $R^n$. Assuming that $g\in L_1(R^n)$ and that the nonzero vector of the first moment of $K$ is finite we prove the existence and uniqueness of a solution of an REMS within a certain class of functions. The renewal density for the solution of this equation is constructed and its properties are investigated. We give a probabilistic interpretation for our results by means of an example from the theory of random walks in $R^n$.
Keywords: renewal, multidimensional space, solvability
Mots-clés : joint motion. 
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N. B. Engibaryan. A renewal equation in a multidimensional space. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 779-785. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a8/

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