Since the 60s of last century Fractional Calculus exhibited a remarkable progress and
presently it is recognized to be an important topic in the scientific arena. This survey …

We develop a statistical theory for a continuous time approximately log‐normal fractional
stochastic volatility model to examine whether the volatility is rough, that is, whether the …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

Rough volatility models are continuous time stochastic volatility models where the volatility
process is driven by a fractional Brownian motion with the Hurst parameter smaller than half …

Fractional Calculus (FC) was a bright idea of Gottfried Leibniz originating in the end of the
seventeenth century. The topic was developed mainly in a mathematical framework, but …

Tempered fractional Brownian motion is obtained when the power law kernel in the moving
average representation of a fractional Brownian motion is multiplied by an exponential …

Let Z denote a Hermite process of order q≥ 1 and self-similarity parameter H∈(1 2, 1). This
process is H-self-similar, has stationary increments and exhibits long-range dependence …

Let {u (t, x), t∈[0, T], x∈ ℝ d} be the solution to the linear stochastic heat equation driven by
a fractional noise in time with correlated spatial structure. We study various path properties …

Let B=(B x) x∈ R d be a collection of N (0, 1) random variables forming a real-valued
continuous stationary Gaussian field on R d, and set C (x− y)= E [B x B y]. Let φ: R→ R be …

We expose some recent and less recent results related to the existence and the basic
properties of the solution to the linear stochastic heat equation with additive Gaussian noise …