Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Asymptotic Laws for One-Dimensional Diffusions Conditioned to Nonabsorption

Pierre Collet, Servet Martinez and Jaime San Martin
The Annals of Probability
Vol. 23, No. 3 (Jul., 1995), pp. 1300-1314
Stable URL: http://www.jstor.org/stable/2244874
Page Count: 15
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Laws for One-Dimensional Diffusions Conditioned to Nonabsorption
Preview not available

Abstract

If (Xt) is a one-dimensional diffusion corresponding to the operator L = 1/2∂xx - α∂x starting from $x > 0$ and Ta is the hitting time of a, we prove that under suitable conditions on the drift coefficient the following limit exists: $\forall s > 0, \forall A \in \mathscr{F}_s, \lim_{t\rightarrow\infty} \mathbb{P}_x(X \in A\mid T_0 > t)$. We characterize this limit as the distribution of an h-like process, h satisfying Lh = - η h, h(0) = 0, h'(0) = 1, where $\eta = -\lim_{t\rightarrow\infty}(1/t)\log\mathbb{P}_x(T_0 > t)$. Moreover, we show that this parameter η can only take two values: η = 0 or $\eta = \underline{\lambda}$, where $\underline{\lambda}$ is the smallest point of increase of the spectral distribution of the operator L* = 1/2∂xx + ∂x(α·).

Page Thumbnails

  • Thumbnail: Page 
1300
    1300
  • Thumbnail: Page 
1301
    1301
  • Thumbnail: Page 
1302
    1302
  • Thumbnail: Page 
1303
    1303
  • Thumbnail: Page 
1304
    1304
  • Thumbnail: Page 
1305
    1305
  • Thumbnail: Page 
1306
    1306
  • Thumbnail: Page 
1307
    1307
  • Thumbnail: Page 
1308
    1308
  • Thumbnail: Page 
1309
    1309
  • Thumbnail: Page 
1310
    1310
  • Thumbnail: Page 
1311
    1311
  • Thumbnail: Page 
1312
    1312
  • Thumbnail: Page 
1313
    1313
  • Thumbnail: Page 
1314
    1314