17 citations · 24 across the 6 of their papers we have counts for
6 papers · 1 filter
The Order Barrier for Strong Approximation of Rough Volatility Models
Andreas Neuenkirch, Taras Shalaiko
We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter . Our met…
Integral representation with respect to fractional Brownian motion under a log-Hölder assumption
Taras Shalaiko, Georgiy Shevchenko
We show that if a random variable is the final value of an adapted log-Hölder continuous process, then it can be represented as a stochastic integral with respect to a fractional B…
The relation between mixed and rough SDEs and its application to numerical methods
Andreas Neuenkirch, Taras Shalaiko
We study the relationship between mixed stochastic differential equations and the corresponding rough path equations driven by standard Brownian motion and fractional Brownian moti…
Convergence of solutions of mixed stochastic delay differential equations with applications
Yuliya Mishura, Taras Shalaiko, Georgiy Shevchenko
The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a -Hölder continuous process with (e.g. a fractional Brown…
Existence of density for solutions of mixed stochastic equations
Taras Shalaiko, Georgiy Shevchenko
We consider a mixed stochastic differential equation driven by independent multidimensional Wiener process and fractional Bro…
Malliavin regularity of solutions to mixed stochastic differential equations
Georgiy Shevchenko, Taras Shalaiko
For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the Malliavin derivative of its solut…