We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly, a correction term in the second level of the limiting rough path which is identified as the average stochastic area on a regeneration interval. A few applications include random walks in random environment and additive functionals of recurrent Markov chains. The result is formulated in the p-variation settings, where a rough path version of Donsker’s Theorem is available under the second moment condition. The key renewal theorem is applied to obtain an optimal moment condition.

Orenshtein, T. (2021). Rough invariance principle for delayed regenerative processes. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 26 [10.1214/21-ECP406].

Rough invariance principle for delayed regenerative processes

Orenshtein T.
2021

Abstract

We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly, a correction term in the second level of the limiting rough path which is identified as the average stochastic area on a regeneration interval. A few applications include random walks in random environment and additive functionals of recurrent Markov chains. The result is formulated in the p-variation settings, where a rough path version of Donsker’s Theorem is available under the second moment condition. The key renewal theorem is applied to obtain an optimal moment condition.
Articolo in rivista - Articolo scientifico
Area anomaly; Invariance principle; Key renewal theorem; P-variation; Random walks in random environment; Regenerative process; Rough paths;
English
Orenshtein, T. (2021). Rough invariance principle for delayed regenerative processes. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 26 [10.1214/21-ECP406].
Orenshtein, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/362304
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