Multiparameter Processes: An Introduction to Random Fields

By Davar Khoshnevisan. 2002

264 citations recorded by the source corpus.

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Citations in the corpus

Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise (2007, methodology): “2 . According to Theorem 4.7.1 of Khoshnevisan [ K02 , Chapter 11], given a random set E in Rn whose codimension is strictly between 0 and n,”
Martingale proofs of many-server heavy-traffic limits for Markovian queues ∗ (2007, background): “For supporting theory at this point, see Theorem 17.24 and Proposition 7.9 of Kallenberg [35] and §7.4 of Daley and Vere-Jones [17].”
Potential theory for hyperbolic SPDEs (2004, methodology): “The latter is a complete, right continuous, commuting filtration (see [10], Chapter 7, Theorem 2.”
Joint continuity of the local times of fractional Brownian sheets (2008, background): “[17]) that, for every T ∈ A such that T ⊂ I , B has almost surely a local time L(x,T ) that is continuous for all x ∈ R .”
Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields (2009, background): “[12]), we may and will assume F is compact and let M > 0 be a constant such that F ⊆ [−M,M ]d.”
Random Choice over a Continuous Set of Options (2013, background): “Ω eΛ(dx) )−1 (13) is a normalizing constant.”
Harmonic analysis of additive Lévy processes (2007, methodology): “[These assertions follow, for example, from Corollary 3.2.1 on page 379, and Lemma 3.4.1 on page 383 of Khoshnevisan (2002).]”
Hitting properties of parabolic s.p.d.e.’s with reflection (2004, methodology): “Our approach to proving this theorem uses a classical discretization technique [4].”
Sample Path Properties of Anisotropic Gaussian Random Fields (2009, methodology): “133] or [49]) states that dimH E = dimc(E) for every compact set E in R .”