Bounding the Solutions to Some SDEs via Ergodic Theory

Abstract

In this note we consider autonomous SDEs admitting smooth invariant measures. We present a method in finding (almost everywhere) good bounds for $\sup \{\Vert X_t\Vert :t\in [0,T]\}$ for strong solutions $X_{\cdot }$ to such SDEs, which in many cases are optimal bounds. In some situation (especially in one-dimensional SDEs' cases), the discarded measure-zero set can be chosen to be a measure-zero set of the underlying Brownian motion uniform for all initial points $X_0=x$.

8 pages

References in corpus (2)

• Bounding Ornstein-Uhlenbeck Processes and Alikes
• Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients

Cited by in corpus (1)

• Bounding Ornstein-Uhlenbeck Processes and Alikes