## The Annals of Probability

### Asymptotic Behavior of Elementary Solutions of One-Dimensional Generalized Diffusion Equations

#### Abstract

We give the asymptotic estimate for large $t$ of elementary solutions of one-dimensional generalized diffusion equations with regularly varying Green functions. As a corollary we obtain the precise asymptotic behavior of the semigroup $T_tf(x)$ for all $f \in L_1(dm)$ if the speed measure function $m(x)$ is regularly varying as $x \rightarrow \pm \infty$.

#### Article information

Source
Ann. Probab., Volume 13, Number 3 (1985), 698-715.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992904

Digital Object Identifier
doi:10.1214/aop/1176992904

Mathematical Reviews number (MathSciNet)
MR799418

Zentralblatt MATH identifier
0574.60083

JSTOR

#### Citation

Minami, Nariyuki; Ogura, Yukio; Tomisaki, Matsuyo. Asymptotic Behavior of Elementary Solutions of One-Dimensional Generalized Diffusion Equations. Ann. Probab. 13 (1985), no. 3, 698--715. doi:10.1214/aop/1176992904. https://projecteuclid.org/euclid.aop/1176992904