Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 3 (1998) > Paper 8 open journal systems 


Estimates for the Derivative of Diffusion Semigroups

L. A. Rincon, University of Wales Swansea


Abstract
Let ${P_t}_{tge 0}$ be the transition semigroup of a diffusion process. It is known that $P_t$ sends continuous functions into differentiable functions so we can write $DP_tf$. But what happens with this derivative when $tto 0$ and $P_0f=f$ is only continuous ?. We give estimates for the supremum norm of the Fr'echet derivative of the semigroups associated with the operators ${cal A}+V$ and ${cal A}+Zcdotnabla$ where ${cal A}$ is the generator of a diffusion process, $V$ is a potential and $Z$ is a vector field.


Full text: PDF

Pages: 65-74

Published on: August 18, 1998
Bibliography
  1. Da Prato, G. and Zabczyk, J. (1992) Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications 44. Cambridge University Press. Math Review 95g:60073
  2. Da Prato, G. and Zabczyk, J. (1997) Differentiability of the Feynman-Kac Semigroup and a Control Application. Rend. Mat. Acc. Lincei s. 9, v. 8, 183-188. Math. Review number not available.
  3. Elworthy, K. D. (1982) Stochastic Differential Equations on Manifolds. Cambridge University Press. Math Review 84d:58080
  4. Elworthy, K. D. and Li, X. M. (1994) Formulae for the Derivative of Heat Semigroups. Journal of Functional Analysis 125, 252-286. Math Review 95j:60087
  5. Elworthy, K. D. and Li, X. M. (1993) Differentiation of Heat Semigroups and applications. Warwick Preprint 77. Math. Review number not available.
  6. Li, X.-M. (1992) Stochastic Flows on Noncompact Manifolds. Warwick University Ph.D. Thesis. Math. Review number not available.
  7. Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag. New York. Math Review 85g:47061
  8. Rincon, L. A. (1994) Some Formulae and Estimates for the Derivative of Diffusion Semigroups. Warwick MSc. Dissertation. Math. Review number not available.
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X