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.
Original language | English |
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Article number | 27 |
Pages (from-to) | 1-35 |
Number of pages | 36 |
Journal | Electronic Journal of Probability |
Volume | 26 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Fluctuation fields
- Higher-order fields
- Orthogonal polynomials
- Self-duality