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42 On Growth in a Random Environment I

By Gerhard Kelier and Göxz Ker Stinq


Abstract: In this paper we study the asymptotic behavior of the solution of the stochastic differential equation U*a = q(Xt)dt + og(Xa)dWa, where g is some positive function. It turns out that in several respects the stochastic behavior of * " depends on whether q (t) is growing slower than t/Log t or not. There are differences regard.ing the rate of growth of if compared with the rat.e in the deterministic situation (o = O) , as well as asymptotic normality and so on

Year: 2011
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