Kolmogorov Equations For Stochastic Pdes

By Giuseppe Da Prato. 2004

300 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f35d2bffdd0618bf8139424434c307cc11094f64

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Citations in the corpus

Existence of strong solutions for stochastic porous media equation under general monotonicity conditions (2007, unknown): “[7], [9]).”
Elliptic and parabolic equations for measures (2009, background): “, the book [67]), especially connected with stochastic partial differential equations (see [11], [52], [57], [58], [62], [63], [70], [74], [79], [82], [90], [91], [128], [150], [163]), infinite gradient systems, Gibbs measures, and stochastic quantization (see [5], [6], [56], [83], [85], [86], [96],”
Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise (2008, result): “[5, 6, 7, 11] and references therein), but comparable results do not seem to be available in the more general jump case considered here.”
Strong uniqueness for SDEs in Hilbert spaces with nonregular drift (2014, unknown): “Z H u(x+sei)ϕ(x)γ(dx)− Z H u(x)ϕ(x)γ(dx) . But by the Cameron–Martin theorem the image measure Tsei(γ) of γunder the translation x→x+sei is absolutely continuous with respect to γwith density (cf. [10], Section 1.2.3) asei(x)=e 2sλihei,xi−s2λi. Hence, the diﬀerence of the two integrals on the right”
On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics (2009, background): “The so-called mild solution [19] of (5) is a generalized process”
Well Posedness and Asymptotic Behavior for Stochastic Reaction-Diffusion Equations with Multiplicative Poisson Noise (2009, unknown): “[10].”
Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift (2011, unknown): “We follow [DZ92], [DZ02], [Da04] and assume Hypothesis 1 A : D(A) ⊂ H → H is a negative definite self-adjoint operator and (−A)−1+δ, for some δ ∈ (0, 1), is of trace class.”
Introduction to stochastic partial differential equations (2008, background): “Under assumptions (1) and (2) above, let”
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient (2017, background): “In the case of an additive noise, it has been the object of several studies, see [11], [19], [15], [34], [44] and the references therein.”