Multidimensional Stochastic Processes as Rough Paths: Markov processes

  title={Multidimensional Stochastic Processes as Rough Paths: Markov processes},
  author={Peter K. Friz and Nicolas Victoir},
Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter H (1/3 < H <= 1/2) under the ellipticity assumption at the
Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes
Since T. Lyons invented rough path theory, one of its most successful applications is a new proof of Freidlin-Wentzell's large deviation principle for diffusion processes. In this paper we extend
Integrability Estimates for Gaussian Rough Differential Equations
It is deduced that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H>1/4.
L\'evy area of fractional Ornstein-Uhlenbeck process and parameter estimation
In this paper, we study the estimation problem of an unknown drift parameter matrix for fractional Ornstein-Uhlenbeck process in multi-dimensional setting. By using rough path theory, we propose
On the Uniqueness of Signature Problem through a Strengthened Le Jan-Qian Approximation Scheme
The goal of this paper is to simplify and strengthen the Le Jan-Qian approximation scheme of studying the uniqueness of signature problem to a non-Markov setting. We establish a general framework for
The uniqueness of signature problem in the non-Markov setting
Quasi-sure Existence of Gaussian Rough Paths and Large Deviation Principles for Capacities
We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation
Large deviation principle for certain spatially lifted Gaussian rough path
In rough stochastic PDE theory of Hairer type, rough path lifts with respect to the space variable of two-parameter continuous Gaussian processes play a main role. A prominent example of such
Order book models, signatures and numerical approximations of rough differential equations
A mathematical model of an order driven market where traders can submit limit orders and market orders to buy and sell securities is constructed and the notion of no free lunch of Harrison and Kreps and Jouini and Kallal is adapted and a no-arbitrage theorem is proved.