Densities for rough differential equations under Hörmander’s condition

Abstract

We consider stochastic differential equations d Y D V .Y / dX driven by a multidimensional Gaussian process X in the rough path sense [T.Lyons, Rev. Mat.Iberoamericana 14, (1998), 215-310].Using Malliavin Calculus we show that Y t admits a density for t 2 .0;T provided (i) the vector fields V D .V 1 ; : : : ; V d / satisfy Hörmander's condition and (ii) the Gaussian driving signal X satisfies certain conditions.Examples of driving signals include fractional Brownian motion with Hurst parameter H > 1=4, the Brownian bridge returning to zero after time T and the Ornstein-Uhlenbeck process.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 131 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.