Higher order fluctuation fields and orthogonal duality polynomials
Mario Ayala (TU Delft - Applied Probability)
Gioia Carinci (Università di Modena e Reggio Emilia)
Frank Redig (TU Delft - Applied Probability)
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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.
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