Markov Processes: Characterization and Convergence

By S. Ethier, Thomas G. Kurtz. 2005

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Citations in the corpus

Computation with finite stochastic chemical reaction networks (2008, background): “Consider the Markov chain restricted to states 1, . . . , l.”
On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise (2015, methodology): “her hand, since P is a measure on a Polish space D(R+,Rd), it is tight, and in particular for any ε > 0, T > 0 there exists a compact set Kε,T ⊂ Rd such that P(Xs ∈ Kε,T) ≥ 1− ε, s ∈ [0,T]; see [EK86], Section 3.5. Combining these two observations we easily get the required stochastic continui”
Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic (2010, methodology): “17 of Chapter 2 of [10]), we get for T > 0,”
Weak and strong solutions of general stochastic models (2013, background): “ α and CS2 α are algebras.) Suppose (Xn,Y) ∈ S1 ×S2, Xn is C-compatible with Y, (Xn,Y) ⇒ (X,Y). Then Xis C-compatible with Y. Remark 3.3 With reference to the continuous mapping theorem (for example, Ethier and Kurtz (1986), Corollary 3.1.9), the continuity assumption on the functions generating BS1”
Survival probabilities for branching Brownian motion with absorption (2007, background): “The main reference for the theory on weak convergence necessary in this section is Ethier and Kurtz [7].”
On the extinction of Continuous State Branching Processes with catastrophes (2013, background): “is the compensated measure of N 1. Even though the process in (9) is a local martingale, we can dene a localized version of the corresponding martingale problem as in Chapter 4.6 of Ethier and Kurtz [15]. We leave the details to the reader. From pathwise uniqueness, we deduce that the solution of (5”
Contributions to the Hypergeometric Function Theory of Heckman and Opdam: Sharp Estimates, Schwartz Space, Heat Kernel (2006, methodology): “In order to apply the Hille-Yosida Theorem (see [9] Theorem 2 .”
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation (2010, background): “Thus it follows from the Markov property and [22], Theorem 2 (see also [20], Corollary 3.”
On the notion(s) of duality for Markov processes (2012, methodology): “ moment dualities to the context of measure-valued processes, see for example [DK82, BLG03, DK96, DG14, EK95]. Moment dualities can be used to show uniqueness of solutions of Martingale problems, see [EK86], section 4, which has been applied for example in the context of SPDEs, [AT00]. 6 Example 1.4”
Large graph limit for an SIR process in random network with heterogeneous connectivity (2010, unknown): “, [11], page 104) and Step 1, the distributions of (μ,μ,μ), for n ∈ N∗, form a relatively compact family of bounded measures on D(R+, M(3)0,A), and so do the laws of the stopped processes (μ (n),S ·∧τn ε ,μ (n),IS ·∧τn ε ,μ (n),RS ·∧τn ε )n∈N∗ [recall (3.”