Zobrazeno 1 - 10
of 261
pro vyhledávání: '"Dalang, Robert C."'
Autor:
Dalang, Robert C., Sanz-Solé, Marta
We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniquen
Externí odkaz:
http://arxiv.org/abs/2410.23995
We formulate the optimal control problem for a sailboat that seeks to reach an upwind buoy, under the hypothesis that the wind speed is constant and the wind direction is a Brownian motion. The yacht moves in $\mathbb{R}^2$ and the target is a ball o
Externí odkaz:
http://arxiv.org/abs/2404.03773
Autor:
Dalang, Robert C., Sanz-Solé, Marta
This book is an introduction to the theory of stochastic partial differential equations (SPDEs), using the random field approach pioneered by J.B. Walsh (1986). The volume consists of two blocks: the core matter (Chapters 1 to 5) and the appendices (
Externí odkaz:
http://arxiv.org/abs/2402.02119
Autor:
Dalang, Robert C., Pu, Fei
We study the hitting probabilities of the solution to a system of $d$ stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive $d-6$-dimensional capacity, the solutio
Externí odkaz:
http://arxiv.org/abs/2307.16129
Autor:
Chong, Carsten, Dalang, Robert C.
We consider a class of parabolic stochastic PDEs on bounded domains $D\subseteq\mathbb{R}^d$ that includes the stochastic heat equation, but with a fractional power $\gamma$ of the Laplacian. Viewing the solution as a process with values in a scale o
Externí odkaz:
http://arxiv.org/abs/2006.15817
We study vector-valued solutions $u(t,x)\in\mathbb{R}^d$ to systems of nonlinear stochastic heat equations with multiplicative noise: \begin{equation*} \frac{\partial}{\partial t} u(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+\sigma(u(t,x))\dot{W}(t,
Externí odkaz:
http://arxiv.org/abs/2002.08212
This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The
Externí odkaz:
http://arxiv.org/abs/1911.09793
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