2010/02/28 by Feng-Yu Wang, Feng‐Yu Wang
Economics, Econometrics and Finance · Mathematics · #Combinatorics #Constant (computer programming) #Coupling (piping) #Markov chain #Markov model #Markov property #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Measure (data warehouse) #Ornstein–Uhlenbeck process #Probability measure #Pure mathematics #Random Matrices and Applications #Rank (graph theory) #Semigroup #Statistics #Stochastic differential equation #Stochastic matrix #Stochastic process #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #math.ST #stat.TH
paper · pdf · doi:10.3150/10-bej308
published as Bernoulli 2011, Vol. 17, No. 4, 1136-1158 · Published in at http://dx.doi.org/10.3150/10-BEJ308 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2011/11/01 · arxiv created 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consider the linear stochastic differential equation (SDE) on ℝn: dXt = AXt dt + B dLt, where A is a real n × n matrix, B is a real n × d real matrix and Lt is a Lévy process with Lévy measure ν on ℝd. Assume that ν(dz) ≥ ρ0(z)dz for some ρ0 ≥ 0. If A ≤ 0, Rank(B) = n and ∫_\|z−z0| ≤ ε\ρ0(z)−1 dz< ∞ holds for some z0 ∈ ℝd and some ε > 0, then the associated Markov transition probability Pt(x, dy) satisfies ‖Pt(x, ⋅) − Pt(y, ⋅)‖var ≤ (C(1 + |x − y|))/(√t), x, y ∈ ℝd, t > 0, for some constant C > 0, which is sharp for large t and implies that the process has successful couplings. The Harnack inequality, ultracontractivity and the strong Feller property are also investigated for the (conditional) transition semigroup.