Abstract
Markov transition kernels are perturbed by output kernels with a special emphasis on building mortality into structured population models. A Feynman-Kac formula is derived which illustrates the interplay of mortality with a Markov process associated with the unperturbed kernel.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Arendt, C.J.K. Batty, M. Hieber, F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Birkhäuser, Basel 2001.
L. Arnold, Stochastic Differential Equations: Theory and Applications, John Wiley, New York 1974.
H. Bauer, Probability Theory and Elements of Measure Theory, Academic Press, London 1981.
M. Demuth, J.A. van Casteren, Stochastic Spectral Theory for Selfadjoint Feller Operators, Birkhäuser, Basel 2000.
O. Diekmann, M. Gyllenberg, J.A.J. Metz, H.R. Thieme, On the formulation and analysis of deterministic structured population models. I. Linear theory, J. Math. Biol. 43 (1998), 349–388.
J. Dugundji, Topology, Allyn and Bacon, Boston 1966, Prentice-Hall of India, New Delhi 1975.
S.N. Ethier, T.G. Kurtz, Markov Processes. Characterization and Convergence, Wiley, New York 1986.
W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York 1965.
A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York 1975.
J.A. Goldstein, Semigroups of Linear Operators and Application, Oxford University Press, New York 1985.
M. Gyllenberg, T. Lant, H.R. Thieme, Perturbing dual evolutionary systems by cumulative outputs, Differential Integral Equations 19 (2006), 401–436.
T. Lant, Transition Kernels, Integral Semigroups on Spaces of Measures, and Perturbation by Cumulative Outputs, Dissertation, Arizona State University, Tempe, December 2004.
T. Lant, H.R. Thieme, Markov transition functions and semigroups of measures, Semigroup Forum, to appear.
B. Ø ksendal, Stochastic Differential Equations, Springer, Berlin Heidelberg 1985.
K. Taira, Semigroups, Boundary Value Problems, and Markov Processes, Springer, Berlin Heidelberg 2004.
H.R. Thieme, Positive perturbations of dual and integrated semigroups, Adv. Math. Sci. Appl. 6 (1996) 445–507.
J.A. van Casteren, Generators of Strongly Continuous Semigroups, Pitman, Boston 1985.
Author information
Authors and Affiliations
Corresponding author
Additional information
partially supported by NSF grants DMS-0314529 and SES-0345945
partially supported by NSF grants DMS-9706787 and DMS-0314529
Rights and permissions
About this article
Cite this article
Lant, T., Thieme, H.R. Perturbation of Transition Functions and a Feynman-Kac Formula for the Incorporation of Mortality. Positivity 11, 299–318 (2007). https://doi.org/10.1007/s11117-006-2044-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11117-006-2044-8