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- W2073724897 abstract "Let $G subset mathbb{R}^k$ be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces ${G_i, i =1,ldots, N}$, where $n_i$ and $d_i$ denote the inward normal and direction of constraint associated with $G_i$, respectively. Stability properties of a class of diffusion processes, constrained to take values in $G$, are studied under the assumption that the Skorokhod problem defined by the data ${(n_i,d_i),i = 1,ldots,N}$ is well posed and the Skorokhod map is Lipschitz continuous. Explicit conditions on the drift coefficient, $b(cdot)$, of the diffusion process are given under which the constrained process is positive recurrent and has a unique invariant measure. Define $$mathscr{C}doteq left{ - sum^{N}_{i=1} a_i d_i;a_i ge 0, i in {1,ldots,N} right}.$$ Then the key condition for stability is that there exists $delta in (0,infty)$ and a bounded subset $A$ of $G$ such that for all $x in Gsetminus A, b(x) in mathscr{C}$ and $mathrm{dist} (b(x),partialmathscr{C}) ge delta$, where $partialmathscr{C}$denotes the boundary of $mathscr{C}$." @default.
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- W2073724897 date "2001-04-01" @default.
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- W2073724897 title "On Positive Recurrence of Constrained Diffusion Processes" @default.
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- W2073724897 doi "https://doi.org/10.1214/aop/1008956699" @default.
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