Differential equations driven by Lévy white noise in spaces of Hilbert space-valued stochastic distributions

Meyer‐Brandis, Thilo

doi:10.1080/17442500701661729

Cited by 4 publications

(2 citation statements)

References 26 publications

(53 reference statements)

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“…The relation between polynomial chaos and chaos decompositions in terms of multiple stochastic integrals with respect to power jump martingales [51] is investigated in detail [47]. Chaos decompositions play a role in the study of Lévy white noise and stochastic differential equations driven by Lévy white noise [18,46,50].…”

Section: Generalized Orthogonal Polynomialsmentioning

confidence: 99%

Intertwining and Duality for Consistent Markov Processes

Floreani¹,

Jansen²,

Redig³

et al. 2021

Preprint

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In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which duality and intertwining can be formulated. We prove falling factorial and orthogonal polynomial intertwining relations in a general setting. These intertwinings unite the previously found "classical" and orthogonal self-dualities in the context of discrete particle systems and provide new dualities for several interacting systems in the continuum. We also introduce a new process, the symmetric inclusion process in the continuum, for which our general method applies and yields generalized Meixner polynomials as orthogonal self-intertwiners.

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Section: Generalized Orthogonal Polynomialsmentioning

confidence: 99%

Intertwining and Duality for Consistent Markov Processes

Floreani¹,

Jansen²,

Redig³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, there has been growing interest in stochastic differential equations of the type (C.1) with jump noise terms. As a result, a few related papers [1,39,40,28,29,45,50] and the forthcoming textbook [49] have been written, but mostly with other fields of applications than finance.…”

Section: Appendix C Stochastic Differential Equationsmentioning

confidence: 99%