An approximation scheme for quasi-stationary distributions of killed diffusions
نویسندگان
چکیده
منابع مشابه
Approximation of quasi-stationary distributions for 1-dimensional killed diffusions with unbounded drifts
The theory of Markov processes with an absorbing state is commonly used in stochastic models of biological population, epidemics, chemical reactions and market dynamics. The stationary distributions of such processes are concentrated on the absorbing state and are of poor interest. In constrast, the long time behavior of an absorbed Markov process is well described by the limiting distribution ...
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Quasi-stationary distributions, as discussed in Darroch and Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present...
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The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation’s method of this limit, when the process is a 1-dimensional Itô diffusion whose drift is allowed to explode at the boundary. In a first step, we show how to restrict the study to the case of a dif...
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Consider a reflecting diffusion in a domain in R that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting process and the value of the drift vector has a product form. Moreover, the first component is the symmetrizing measure on the domain for the reflecting dif...
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Given a domain G, a reflection vector field d(·) on ∂G, the boundary of G, and drift and dispersion coefficients b(·) and σ(·), let L be the usual second-order elliptic operator associated with b(·) and σ(·). Under mild assumptions on the coefficients and reflection vector field, it is shown that when the associated submartingale problem is well posed, a probability measure π on Ḡ with π(∂G) = ...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2020
ISSN: 0304-4149
DOI: 10.1016/j.spa.2019.09.010