ON POSITIVE RECURRENCE OF CONSTRAINED DIFFUSION PROCESSES

By Rami Atar, A. Budhiraja, Paul Dupuis. 2001

65 citations recorded by the source corpus.

Let G c R k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G i , i = 1,..., , 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,., , N} is well posed and the Skorokhod map is Lipschitz continuous. Explicit conditions on the drift coefficient, b(.), of the diffusion process are given under which the constrained process is positive recurrent and has a unique invariant measure. Define C =˙ {-Σ α i d i ; α i ≥ 0, i ∈ {1,…,N}}. Then the key condition for stability is that there exists δ ∈ (0, ∞) and a bounded subset A of G such that for all x ∈ G\A, b(x) ∈ C and dist(b(x), ∂C) > δ, where ∂C denotes the boundary of C.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eff0eebd461ac42fe3356e3e6a13857c7a54d5c1

How researchers see this paper

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In Finance

1. Weining Kang
2. Kavita Ramanan
3. A. Budhiraja
4. Tusheng Zhang

In Mathematical Physics

1. Weining Kang
2. Kavita Ramanan
3. A. Budhiraja
4. Daniel Paulin
5. Radosław Adamczak

In Statistics and Probability

1. Weining Kang
2. Kavita Ramanan
3. A. Budhiraja
4. Itai Gurvich
5. Daniel Paulin
6. Radosław Adamczak

Citations in the corpus

• Characterization of stationary distributions of reflected diffusions. (2012, background): “Note that when α ∈ [1,2), the RBM is not a semimartingale.”
• Long time asymptotics for constrained diffusions in polyhedral domains (2007, background): “Under suitable conditions on the drift vector field, existence of a unique invariant probability distribution for this class of diffusions was established in [1].”