Search Results - "Shalaiko, Taras"

The Relation Between Mixed and Rough SDEs and Its Application to Numerical Methods by Neuenkirch, Andreas, Shalaiko, Taras

“…We study the relationship between mixed stochastic differential equations and the corresponding rough path equations driven by standard Brownian motion and…”
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Integral representation with respect to fractional Brownian motion under a log-Hölder assumption by Shalaiko, Taras, Shevchenko, Georgiy

“…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…”
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The maximum rate of convergence for the approximation of the fractional Lévy area at a single point by Neuenkirch, Andreas, Shalaiko, Taras

“…In this note we study the approximation of the fractional Lévy area with Hurst parameter H>1/2, considering the mean square error at a single point as error…”
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Malliavin regularity of solutions to mixed stochastic differential equations by Shevchenko, Georgiy, Shalaiko, Taras

“…For a mixed stochastic differential equation driven by independent fractional Brownian motions and Wiener processes, the existence and integrability of the…”
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Convergence of solutions of mixed stochastic delay differential equations with applications by Mishura, Yuliya, Shalaiko, Taras, Shevchenko, Georgiy

“…The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a γ-Hölder continuous process with γ>1/2 (e.g. a…”
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The Order Barrier for Strong Approximation of Rough Volatility Models by Neuenkirch, Andreas, Shalaiko, Taras

“…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…”
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Integral representation with respect to fractional Brownian motion under a log-H\"{o}lder assumption by Shalaiko, Taras, Shevchenko, Georgiy

“…Modern Stochastics: Theory and Applications 2015, Vol. 2, No. 3, 219-232 We show that if a random variable is the final value of an adapted log-H\"{o}lder…”
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The relation between mixed and rough SDEs and its application to numerical methods by Neuenkirch, Andreas, Shalaiko, Taras

“…We study the relationship between mixed stochastic differential equations and the corresponding rough path equations driven by standard Brownian motion and…”
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Existence of density for solutions of mixed stochastic equations by Shalaiko, Taras, Shevchenko, Georgiy

“…We consider a mixed stochastic differential equation $d{X_t}=a(t,X_t)d{t}+b(t,X_t) d{W_t}+c(t,X_t)d{B^H_t}$ driven by independent multidimensional Wiener…”
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Malliavin regularity of solutions to mixed stochastic differential equations by Shevchenko, Georgiy, Shalaiko, Taras

“…Statistics and Probability Letters 83 (2013), pp. 2638-2646 For a mixed stochastic differential driven by independent fractional Brownian motions and Wiener…”
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Convergence of solutions of mixed stochastic delay differential equations with applications by Mishura, Yuliya, Shalaiko, Taras, Shevchenko, Georgiy

“…The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\gamma$-H\"older continuous process with…”
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