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- Title
A stochastic model for speculative dynamics.
- Authors
Gadat, Sébastien; Miclo, Laurent; Panloup, Fabien
- Abstract
The aim of this paper is to provide a simple model for describing speculative dynamics and to focus on the study of some associated quantities of interest. Starting from a description of individual speculative behaviors, we build a second order non-reversible Markov process, which after simple transformations can be viewed as a turning two-dimensional Gaussian process. Then, our main problem is to obtain some bounds for the persistence rate relative to the return time to a given level. We prove with both spectral and probabilistic methods that this rate is almost proportional to the turning frequency w of the model and provide some explicit bounds. The persistence rate being strongly linked to the quasi-stationary distribution of the problem, we also prove its existence. The main results are established with a careful manipulation of a strongly degenerate hypoelliptic second order Markov operator, which significantly complicates the spectral analysis.
- Subjects
MARKOV processes; GAUSSIAN processes; QUASISTATIC processes; MATHEMATICAL transformations; HYPOELLIPTIC differential equations
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2015, Vol 12, p491
- ISSN
1980-0436
- Publication type
Article