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pro vyhledávání: '"Bignamini, Davide A."'
Let $U,H$ be two separable Hilbert spaces and $T>0$. We consider an SDE which evolves in the Hilbert space $H$ of the form \begin{align} dX(t)=AX(t)dt+\widetilde{\mathscr L}B(X(t))dt+GdW(t), \quad t\in[0,T], \quad X(0)=x \in H, \end{align} where $A:D
Externí odkaz:
http://arxiv.org/abs/2405.14819
In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroups associated with a stochastic partial differential equations. This is done in terms of exponential integrability of Lipschitz funct
Externí odkaz:
http://arxiv.org/abs/2311.04523
Autor:
Bignamini, Davide A., De Fazio, Paolo
In an infinite dimensional separable Hilbert space $X$, we study the realizations of Ornstein-Uhlenbeck evolution operators $\pst$ in the spaces $L^p(X,\g_t)$, $\{\g_t\}_{t\in\R}$ being the unique evolution system of measures for $\pst$ in $\R$. We p
Externí odkaz:
http://arxiv.org/abs/2309.07319
Autor:
Addona, Davide, Bignamini, Davide A.
In this paper, we prove pathwise uniqueness for stochastic differential equations in infinite dimension. Under our assumptions, we are able to consider the stochastic heat equation up to dimension $3$, the stochastic damped wave equation in dimension
Externí odkaz:
http://arxiv.org/abs/2308.05415
In this paper we study two notions of differentiability introduced by P. Cannarsa and G. Da Prato (see [28]) and L. Gross (see [56]) in both the framework of infinite dimensional analysis and the framework of Malliavin calculus.
Externí odkaz:
http://arxiv.org/abs/2308.05004
Autor:
Bignamini, Davide A., Ferrari, Simone
Publikováno v:
Stoch. Anal. Appl., 2024
We consider stochastic reaction-diffusion equations with colored noise and prove Schauder type estimates, which will depend on the color of the noise, for the stationary and evolution problems associated with the corresponding transition semigroup, d
Externí odkaz:
http://arxiv.org/abs/2207.13042
Autor:
Bignamini, Davide A., Ferrari, Simone
Publikováno v:
J. Differential Equations 370:305-345, 2023
We prove Schauder type estimates for solutions of stationary and evolution equations driven by weak generators of transition semigroups associated to a semilinear stochastic partial differential equations with values in a separable Hilbert space.
Externí odkaz:
http://arxiv.org/abs/2205.14388
Autor:
Bignamini, Davide A.
Let $\mathcal{X}$ be a real separable Hilbert space. Let $C$ be a linear, bounded and positive operator on $\mathcal{X}$ and let $A$ be the infinitesimal generator of a strongly continuous semigroup on $\mathcal{X}$. Let $\{W(t)\}_{t\geq 0}$ be a $\m
Externí odkaz:
http://arxiv.org/abs/2110.05271
Autor:
Bignamini, Davide A., Ferrari, Simone
Publikováno v:
In Journal of Differential Equations 15 October 2023 370:305-345
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