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Optimal Control of Stochastic Partial Differential Equations

Title
Optimal Control of Stochastic Partial Differential Equations
Funding
ARC | Discovery Projects
Contract (GA) number
DP0346406
Start Date
2003/01/01
End Date
2003/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0346406

 

  • Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators

    The spectra of the second quantization and the symmetric second quantization of a strict Hilbert space contraction are computed explicitly and shown to coincide. As an application, we compute the spectrum of the nonsymmetric Ornstein-Uhlenbeck operator $L$ associated with the infinite-dimensional Langevin equation $$ dU(t) = AU(t)dt + dW(t), $$ where $A$ is the generator of a strongly continuous semigroup on a Banach space $E$ and $W$ is a cylindrical Wiener process in $E$. In the case of a f...

    Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs

    A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein--Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and $V$-ergodicity are proved for a large class of equations. We also provide computable bounds on the convergence rates and the spectral gap for the Markov semigroups defined by the equations. The bounds turn out to be uniform ...
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