Extending the Wong-Zakai theorem to reversible Markov processes

By Richard F. Bass, Ben M. Hambly, Terry Lyons. 2002

53 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c234325d13a6326b5aa7808925c08e41da4ba616

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

An Introduction to Rough Paths (2003, methodology): “Here, x is a continuous function from [0, 1] to Rd, and the notion of irregularity we use is that of p-variation, as defined by N. Wiener.”
An extension theorem to rough paths (2007, background): ““Canonical” lifts have been constructed for Brownian motion [13,10], fractional Brownian motion with Hurst parameter greater than 1/4 [3,13], free Brownian motion [2,18], and a large class of random paths on fractals [1,8].”
Power Variation and Time Change (2006, unknown): “We also refer to the related work of Lyons on rough paths, see Lyons (1994) and Bass, Hambly, and Lyons (2002) and references given there.”
Semi-martingales and rough paths theory (2005, methodology): “Although the rough path theory is completely deterministic, it has been used for a large class of processes, including Brownian motion, some Gaussian processes in a Banach space [18], fractional Brownian motion [5], free Brownian motion [3], symmetric Markov process [1],.”
Large deviations and support theorem for diffusion processes via rough paths (2002, background): “Bass et al., 1998), even though we do not address applications of this type here. In order to state the main results proved in this paper, we Arst recall several basic notions and Ax the notations as well. We refer to Lyons (1998) and Lyons and Qian (to appear) for further details.”
Discretely sampled signals and the rough Hoff process (2013, methodology): “o be: XD u = 0; u t∗ 0 Xt1 if u∈ [0,t∗ 0); Xt n−1 + u−t∗ n−1 t n−t∗ n−1 Xt n −Xt n−1 ;Xt n if u∈ [t∗ n−1,tn]. Date: November 13, 2013. 1A partition is a collection of distinct points in [0,1]. We assume that every partition contains the endpoints 0 and 1. Let D[0,1] denote the set of all part”
LÉVY AREA OF WIENER PROCESSES IN BANACH SPACES (2002, background): “The papers [2, 8, 16] establish the same sort of results for a wide range of diffusion processes and also for fractional Brownian motions.”