Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStochastic Maximum Principle for a PDEs with noise and control on the boundary
395
0
0.0
(
0
)
Added by
Giuseppina Guatteri
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Authors
Giuseppina Guatteri
Ask ChatGPT about the research
No Arabic abstract
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a stochastic control problem for an evolution system in an Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle.
rate research
Read More
In this work we first present the existence, uniqueness and regularity of the strong solution of the tidal dynamics model perturbed by Levy noise. Monotonicity arguments have been exploited in the proofs. We then formulate a martingale problem of Stroock and Varadhan associated to an initial value control problem and establish existence of optimal controls.
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the stochastic maximum principle as the necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. The stochastic linear quadratic problem in this setting is also discussed.
Consider the stochastic heat equation $partial_tu=mathscr{L}u+lambdasigma(u)xi$, where $mathscr{L}$ denotes the generator of a L{e}vy process on a locally compact Hausdorff Abelian group $G$, $sigma:mathbf{R}tomathbf{R}$ is Lipschitz continuous, $lambdagg1$ is a large parameter, and $xi$ denotes space-time white noise on $mathbf{R}_+times G$. The main result of this paper contains a near-dichotomy for the (expected squared) energy $mathrm{E}(|u_t|_{L^2(G)}^2)$ of the solution. Roughly speaking, that dichotomy says that, in all known cases where $u$ is intermittent, the energy of the solution behaves generically as $exp{operatorname {const}cdot,lambda^2}$ when $G$ is discrete and $geexp{operatorname {const}cdot,lambda^4}$ when $G$ is connected.
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum condition, we reformulate the original control problem as a new one. Three algorithms are proposed to solve the new control problem. Numerical results for different examples demonstrate the effectiveness of our proposed algorithms, especially in high dimensional cases. And an important application of this method is to calculate the sub-linear expectations, which correspond to a kind of fully nonlinear PDEs.
In this paper, the optimal control problem of neutral stochastic functional differential equation (NSFDE) is discussed. A class of so-called neutral backward stochastic functional equations of Volterra type (VNBSFEs) are introduced as the adjoint equation. The existence and uniqueness of VNBSFE is established. The Pontryagin maximum principle is constructed for controlled NSFDE with Lagrange type cost functional.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
