Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T15:11:54.224Z Has data issue: false hasContentIssue false
  • English
  • Français

A diffusion model with loss of particles

Published online by Cambridge University Press:  01 July 2016

Lech S. Papież  and
George A. Sandison
Lech S. Papież*
Affiliation:
Manitoba Cancer Foundation and University of Manitoba
George A. Sandison*
Affiliation:
Manitoba Cancer Foundation and University of Manitoba
*
Postal address for both authors; Department of Medical Physics, Manitoba Cancer Foundation, 100 Olivia Street, Winnipeg, Manitoba, Canada R3E 0V9 or Department of Physics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
Postal address for both authors; Department of Medical Physics, Manitoba Cancer Foundation, 100 Olivia Street, Winnipeg, Manitoba, Canada R3E 0V9 or Department of Physics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamical behaviour of particles which undergo diffusion with annihilation is modelled by a parabolic (Fokker–Planck) equation. Fundamental, closed-form solutions of this equation, identified with transition densities of the underlying stochastic process, are calculated by utilizing specific methods of probability measures on functional spaces and evolution semigroups.

Keywords

DIFFUSION WITH ANNIHILATIONWIENER MEASUREORNSTEIN–UHLENBECK BRIDGEEVOLUTION SEMIGROUPS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 533 - 547
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Eyges, L. (1948) Phys. Rev. 79, 1534.CrossRefGoogle Scholar
Hida, T. (1975) Brownian Motion. Springer-Verlag, New York.Google Scholar
Ito, K. and Mckean, H. Jr. (1965) Diffusion Processes and Their Sample Paths. Springer-Verlag, Berlin.Google Scholar
John, F. (1982) Partial Differential Equations. Springer-Verlag, New York.CrossRefGoogle Scholar
Kac, M. (1951) On some connections between probability theory and differential and integral equations. Proc. 2nd Berkeley Symp. Math. Statist. Prob., 189–215.Google Scholar
Karlin, S. and Taylor, M. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
Krein, S. G. (1971) Linear Differential Equations in Banach Space. American Mathematical Society, Providence, Rhode Island.Google Scholar
Reed, M. and Simon, B. (1975) Methods of Modern Mathematical Physics II. Academic Press, New York.Google Scholar
Rudin, W. (1973) Functional Analysis. McGraw-Hill, New York.Google Scholar
Sandison, G. A. and Papiez, L. S. (1990) Phys. Med. Biol. To appear.Google Scholar
Ventzel, A. (1981) A Course in the Theory of Stochastic Processes. McGraw-Hill, New York.Google Scholar