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.

Stability in Distribution of Mild Solutions to Stochastic Partial Differential Delay Equations with Jumps

Jianhai Bao, Aubrey Truman and Chenggui Yuan
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 465, No. 2107 (Jul. 8, 2009), pp. 2111-2134
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/30245453
Page Count: 24
  • Read Online (Free)
  • 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.
Stability in Distribution of Mild Solutions to Stochastic Partial Differential Delay Equations with Jumps
Preview not available

Abstract

The existence, uniqueness and some sufficient conditions for stability in distribution of mild solutions to stochastic partial differential delay equations with jumps are presented. The principle technique of our investigation is to construct a proper approximating strong solution system and carry out a limiting type of argument to pass on stability of strong solutions to mild ones. As a consequence, stability results of Basak et al. (Basak et al. 1999 J. Math. Anal. Appl. 202, 604-622) and Yuan et al. (Yuan et al. 2003 Syst. Control Lett. 50, 195-207) are generalized to cover a class of much more general stochastic partial differential delay equations with jumps in infinite dimensions. In contrast to the almost sure exponential stability in Ichikawa (Ichikawa 1982 J. Math. Anal. Appl. 90, 12-44) and Luo & Liu (Luo & Liu 2008 Stoch. Proc. Appl. 118, 864-895) and the moment exponential stability in Luo & Liu, we present a new result on the stability in distribution of mild solutions. Finally, an example is given to demonstrate the applicability of our work.

Page Thumbnails

  • Thumbnail: Page 
2111
    2111
  • Thumbnail: Page 
2112
    2112
  • Thumbnail: Page 
2113
    2113
  • Thumbnail: Page 
2114
    2114
  • Thumbnail: Page 
2115
    2115
  • Thumbnail: Page 
2116
    2116
  • Thumbnail: Page 
2117
    2117
  • Thumbnail: Page 
2118
    2118
  • Thumbnail: Page 
2119
    2119
  • Thumbnail: Page 
2120
    2120
  • Thumbnail: Page 
2121
    2121
  • Thumbnail: Page 
2122
    2122
  • Thumbnail: Page 
2123
    2123
  • Thumbnail: Page 
2124
    2124
  • Thumbnail: Page 
2125
    2125
  • Thumbnail: Page 
2126
    2126
  • Thumbnail: Page 
2127
    2127
  • Thumbnail: Page 
2128
    2128
  • Thumbnail: Page 
2129
    2129
  • Thumbnail: Page 
2130
    2130
  • Thumbnail: Page 
2131
    2131
  • Thumbnail: Page 
2132
    2132
  • Thumbnail: Page 
2133
    2133
  • Thumbnail: Page 
2134
    2134