کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602763 1336937 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Survival in a quasi-death process
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Survival in a quasi-death process
چکیده انگلیسی

We consider a Markov chain in continuous time with one absorbing state and a finite set S of transient states. When S is irreducible the limiting distribution of the chain as t→∞, conditional on survival up to time t, is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which S may be reducible, and show that it remains valid if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on S has geometric (but not, necessarily, algebraic) multiplicity one. The result is then applied to pure death processes and, more generally, to quasi-death processes. We also show that the result holds true even when the geometric multiplicity is larger than one, provided the irreducible subsets of S satisfy an accessibility constraint. A key role in the analysis is played by some classic results on M-matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 4, 1 August 2008, Pages 776-791