Publication

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic
2014
Journal Articles

Abstract

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures.

Official source

https://infoscience.epfl.ch/entities/publication/84bc34b5-4ceb-4270-ac77-145ae4ae832e

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Damir Filipovic
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/84bc34b5-4ceb-4270-ac77-145ae4ae832e

About this result

Related concepts (17)

Hilbert space

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space.

Poisson point process

In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.

Random measure

In probability theory, a random measure is a measure-valued random element. Random measures are for example used in the theory of random processes, where they form many important point processes such as Poisson point processes and Cox processes. Random measures can be defined as transition kernels or as random elements. Both definitions are equivalent. For the definitions, let be a separable complete metric space and let be its Borel -algebra. (The most common example of a separable complete metric space is ) A random measure is a (a.

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