Inspired by the works in [2] and [11] we introduce what we call k-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of discrete analogue of powers of the well-known density fluctuation field. We show that the weak limit of the k-th order field satisfies a recursive martingale problem that corresponds to the SPDE associated with the kth-power of a generalized Ornstein-Uhlenbeck process.

Higher order fluctuation fields and orthogonal duality polynomials / Ayala, M.; Carinci, G.; Redig, F.. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 26:none(2021), pp. 1-35. [10.1214/21-EJP586]

Higher order fluctuation fields and orthogonal duality polynomials

Carinci G.;Redig F.
2021

Abstract

Inspired by the works in [2] and [11] we introduce what we call k-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of discrete analogue of powers of the well-known density fluctuation field. We show that the weak limit of the k-th order field satisfies a recursive martingale problem that corresponds to the SPDE associated with the kth-power of a generalized Ornstein-Uhlenbeck process.
2021
26
none
1
35
Higher order fluctuation fields and orthogonal duality polynomials / Ayala, M.; Carinci, G.; Redig, F.. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 26:none(2021), pp. 1-35. [10.1214/21-EJP586]
Ayala, M.; Carinci, G.; Redig, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1257341
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