Evolution equations driven by a fractional Brownian motion

By Bohdan Maslowski, David Nualart. 2003

227 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/3fb0507ad1e20ee9fa35f0b8aaf8ec1ee123fbd9

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Citations in the corpus

Ergodicity of the Infinite Dimensional Fractional Brownian Motion (2011, background): “Meanwhile there are many articles dealing with existence of solutions of ordinary or partial stochastic differential equations driven by a fractional Brownian motion, see for instance [7,10, 18 ,19,21,24] among others.”
Ergodicity of stochastic differential equations driven by fractional Brownian motion (2003, background): “α(1−2α). 6.2 Inﬁnite-dimensional case In the case where the phase space for (SDE) is inﬁnite-dimensional, the question of global existence of solutions is technically more involved and was tackled in [MN02]. Another technical difﬁculty arises from the fact that one mi ght want to take for σan operat”
Young Integrals and SPDEs (2004, unknown): “e In the non-linear case, the same kind of results are available in ( MN03 ).”
Stochastic heat equation driven by fractional noise and local time (2007, background): “The same result holds when one adds to the above equation a nonlinearity of the form b(t, x, u), where b satisfies the usual linear growth and Lipschitz conditions in the variable u, uniformly with respect to (t, x) (see Maslowski and Nualart in [9]).”
Existence of mild solutions for fractional evolution equations (2013, background): “From [19], we know that A generates an analytic, noncompact semigroup {T (t)}t≥0 on L(2)(R).”
Functional differential equations in Hilbert spaces driven by a fractional Brownian motion (2012, methodology): “We will refer the reader to the papers of Zahle [12], Nualart and R˘ a¸ scanu [8] and Nualart and Maslowski [ 6 ] for the general theory.”
Stochastic delay fractional evolution equations driven by fractional Brownian motion (2014, background): “Maslowski and Nualart [10] studied nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter H > 12 and nuclear covariance operator.”
Non-linear rough heat equations (2009, methodology): “In the Young integration context, some recent efforts have also been made in order to define solutions to parabolic [24,35] or wave type [42] equations.”
Variational solutions for partial differential equations driven by a fractional noise (2006, background): “…multiplicative, multiparameter fractional noise and estimated the Lyapunov exponents of the corresponding solutions; finally, the authors of [18] and [38] have proved the existence and the uniqueness of mild solutions to various classes of stochastic evolution equations driven by a fractional…”
The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion (2011, background): “(Nualart [17]) For φ ∈ L1/H([0, T ]), H(2H − 1) ∫ T 0 ∫ T 0 |φ(r)||φ(u)||r − u|2H−2drdu ≤ cH‖φ‖2L1/H([0,T ]).”
Stochastic Heat Equation with Multiplicative Fractional-Colored Noise (2008, background): “n. What happens when the space-time white noise is replaced by a noise which is fractional in time, but continues to be white in space? This situation has been studied in several papers such as [14], [24], [29], [34] and recently in [1]. In this case, a necessary and suﬃcient condition for the exist”
Malliavin Calculus for Fractional Delay Equations (2009, methodology): “When the Hölder regularity of the driving noise is larger than 1=2, this has been achieved thanks to Young integrals [9] or fractional integration [11] techniques.”