## Evolution equations driven by a fractional white noise in spaces of abstract stochastic distributions |

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abstract stochastic distributions additive noise arbitrary Hurst parameter Banach spaces Bender bounded linear operator bounded operator C_i,_ C_i._ Cauchy problem cilindrical fractional Brownian Co-semigroup consider the following continuous function define Definition denote differ from line Elliot equation with multiplicative equations in infinite estimate 2.4 Evolution Equations Driven existence and uniqueness f S(t fc=i Filinkov and Sorensen fractional Brownian motion fractional white noise fs(t heat equation Hermite polynomials Hermite transform Hilbert space Hoek hypothesis inductive limit infinite dimension infinite-dimensional Kondratiev spaces Lemma Lipschitz function Marcelo F Métodos mild solution motion with parameter multiplicative noise nonlinear NT2 sup orthonormal basis parameter H Paulo Proof of Theorem prove Theorem 3.1 real numbers rewrite equation Rojas-Medar sequence of real spaces of abstract stochastic calculus stochastic equations stochastic evolution equations stochastic partial strict contraction strong solution strongly continuous semigroup study stochastic t-OC white noise analysis white noise theory Wick product