Corrections to: Extending the martingale measure stochastic integral with applications to spatially homogeneous S.P.D.E. 's

By Robert C. Dalang. 2001

233 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/916b231fdd66a24df2e80b20b1c91b6f4ae74839

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Citations in the corpus

Nonlinear stochastic wave and heat equations (2000, background): “In fact the referee of the present paper has indicated that Dalang [ 2 ] has recently extended the theory of stochastic integration with respect to martingale measures to a class of distribution-valued processes, and applied this to 3 dimensional wave equations.”
The Cauchy problem for a nonlinear stochastic wave equation in any dimension (2002, background): “Dalang [ 2 ] has recently extended this theory a class of distribution-valued integrands, and applied this to 3 dimensional wave equations.”
Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case (2008, result): “In fact for coloured noise in higher dimensions the results in (MPS06) did not even come close to the known results on pathwise uniqueness for Lipschitz continuous coefficients ( Dal99 )–see the discussion after Remark 1.5 in (MPS06).”
Affine Volterra processes (2017, background): “t≤ T, n≥ 2, where one can take c= 2p−1(Tp/2+C p)cLIPkKk p−2 L2(0,T) with Cpthe constant from the BDG inequality and cLIP a common Lipschitz constant for band σ. The extended Gronwall’s lemma given in Dalang (1999, Lemma 15) now yields that the series X n≥2 E[|Xn t −X n−1 t | p] 34 converges, uniform”
Intermittence and nonlinear parabolic stochastic partial differential equations (2008, methodology): “In the linearized case [σ≡ 1], that SPDE does not have a randomfield solution [ 14 ; 19].”
Non-linear rough heat equations (2009, background): “urse, one should also have in mind the huge literature concerning the case of evolution equations driven by usual Brownian motion, for which we refer to [8] for the inﬁnite dimensional setting and to [7] for the multiparametric framework. In the particularcase ofthestochastic heatequation driven by ”
Stochastic NonLinear Wave Equations in Local Sobolev Spaces (2010, background): “[6], [7], [8], [10], [12], [13], [14], [22], [23], [25], [26], [27], [28], [29], [30], [32], [35], [36], [37] and references therein) with possible applications in physics (e.”
Gaussian fluctuations for the stochastic heat equation with colored noise (2019, background): “(1.4); see e.g. [10, Chapter 3] for the properties of Stein’s solution. Thus, proceeding in the exact same lines as in this paper, we will get the same rate in these distances. It is known (see, e.g. [4, 18]) that equation (1.1) has a unique mild solution {u(t,x) : t ≥ 0,x ∈ Rd}, in the sense that i”