Property rights of landholders in non-captive wildlife and prospects for conservation

In order to reduce the rate of human-induced biodiversity loss of wild species, it has become increasingly important to stem this loss on private and tribal lands and to find effective policies to do this. Some writers believe that granting landholders commercial property rights in wildlife might be effective in dealing with this matter and result in the sustainable use of wildlife. This paper explores this view using economic theory. In doing so, it takes into account the total economic valuation concept. While granting of commercial property rights is found to be effective for conserving some species, it is predicted to be a complete failure as a means of conserving other species. In addition, particular attention is given to the economics of the utilisation and conservation of non-captive fugitive (or mobile) wildlife. The economic theory involved is contrasted and compared with that for the exploitation of open-access resources.

Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.