Stochastic Equations in Infinite Dimensions

By Giuseppe Da Prato, Jerzy Zabczyk. 2008

1,720 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/fe56390b1a218e76d1d128fc43b6dc1e382fa252

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Finance

Citations in the corpus

On the convergence of stochastic transport equations to a deterministic parabolic one (2019, methodology): “Now let W̃ be a cylindrical Wiener process on L2(Td;Rd) (in the sense of [10]): a Gaussian distribution valued process with covariance E [ 〈W̃t, φ〉〈W̃s, ψ〉 ] = (t ∧ s)〈φ,ψ〉 ∀φ,ψ ∈ C(T).”
A moderate deviation principle for 2-D stochastic Navier-Stokes equations (2015, background): “Since the work of Bensoussan and Temam [2], stochastic Navier–Stokes equations have been intensively studied, see [7] for the equation with additive Gaussian noise.”
Large deviations for the Boussinesq equations under random influences (2008, background): “It is a linear symmetric positive covariant operator in the Hilbert space H. We assume that Q1, Q2 and thus Q are trace class (and hence compact [ 8 ]), i.e., tr(Q) 8 ]) from H to H. The norm in the space LQ is defined by |S|2LQ = tr(SQS ∗), where S∗ is the adjoint operator of S.”
Markov selections for the 3D stochastic Navier–Stokes equations (2006, background): “where W is a cylindrical Wiener process on H (see [7] for more details).”
Lower bound technique in the theory of a stochastic differential equation (2006, background): “However, to the best of our knowledge, almost all results (see [1,2,7,10,13]) are devoted to existence and uniqueness of solutions rather than to existence of an invariant measure.”
Large deviation principles for 2-D stochastic Navier–Stokes equations driven by Lévy processes (2009, background): “A good reference for stochastic Navier-Stokes equations driven by additive noise is the book [5] and the references therein.”
Asymptotic stability of nonlinear impulsive stochastic differential equations (2009, methodology): “The existence, uniqueness and asymptotic behavior of solutions of the stochastic differential equations have been considered by many authors (Caraballo and Real (1993), Ichikawa (1982), Khas’minskii (1980), Liu and Truman (2000), Liu and Mao (1998), Taniguchi et al.”
Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps (2008, methodology): “The reader is referred to [8] for a systematic theory about stochastic integrals of this kind.”
Exponential stability for stochastic neutral partial functional differential equations (2009, neutral): “Hence, by the linear growth conditions in (H2), Hölder’s inequality and Burkholder–Davis–Gundy type of inequality for stochastic convolutions [2], for any p > 2 there exists a number c(p, T ) > 0 such that sup 0 s t E ∣∣x(n)(s)∣∣p 3p−1[1− C5∥∥(−A)−α∥∥− C5M1−ατ (T )]−p × {( M0e |ν|T ∣∣φ(0)∣∣+ C5(1+ ‖”