Scaling Limits of Solutions of Linear Evolution Equations with Random Initial Conditions

Miłosz Krupski

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arXiv · 1501.01279

Scaling Limits of Solutions of Linear Evolution Equations with Random Initial Conditions

Miłosz Krupski

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Abstract

We consider a linear equation $\partial_t u = \mathcal{L}u$, where $\mathcal{L}$ is a generator of a semigroup of linear operators on a certain Hilbert space related to an initial condition $u(0)$ being a generalised stationary random field on $\mathbb{R}^d$. We show the existence and uniqueness of generalised solutions to such initial value problems. Then we investigate their scaling limits.

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Miłosz Krupski. 2015-01-06. Scaling Limits of Solutions of Linear Evolution Equations with Random Initial Conditions. https://arxiv.org/abs/1501.01279

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