Displaying similar documents to “Hypercontractivity of solutions to Hamilton-Jacobi equations”

Differentiability of the Feynman-Kac semigroup and a control application

Giuseppe Da Prato, Jerzy Zabczyk (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.

Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation

Giuseppe Da Prato, Arnaud Debussche (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup P t ⁢ φ does exist for any bounded φ ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Uniform exponential ergodicity of stochastic dissipative systems

Beniamin Goldys, Bohdan Maslowski (2001)

Czechoslovak Mathematical Journal

Similarity:

We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in ℝ d with d ≤ 3 .