Self-similar processes are stochastic processes that are invariant in distribution under
suitable time scaling, and are a subject intensively studied in the last few decades. This …

As is well-known, the classical Brownian motion is a stochastic process which is selfsimilar
of index 1/2 and has stationary increments. It is actually the only continuous Gaussian …

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the
Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a …

This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–
Uhlenbeck process driven by fractional Brownian motion, whose observations can be made …

We compute the exact rates of convergence in total variation associated with the 'fourth
moment theorem'by Nualart and Peccati (2005), stating that a sequence of random variables …

In recent years, there has been a substantive interest in rough volatility models. In this class
of models, the local behavior of stochastic volatility is much more irregular than …

For a stochastic differential equation (SDE) driven by a fractional Brownian motion (fBm) with
Hurst parameter H>12, it is known that the existing (naive) Euler scheme has the rate of …

Supplement to “High-frequency analysis of parabolic stochastic PDEs”. This paper is
accompanied by supplementary material in [14]. Section A in [14] gives some auxiliary …

In physics, classical analysis plays a central role. For instance in Newtonian mechanics,
thermodynamics, and electricity, many phenomena are well explained by deterministic …

In this article, we consider the so-called modified Euler scheme for stochastic differential
equations (SDEs) driven by fractional Brownian motions (fBm) with Hurst parameter ⅓< H< …