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20062024
most citedMixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions

64 citations · 320 across the 79 of their papers we have counts for

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Showing 2012Show all

2 papers · 1 filter

math.PR2012★ 15 cited

Stochastic viability and comparison theorems for mixed stochastic differential equations

Alexander Melnikov, Yuliya Mishura, Georgiy Shevchenko

For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent , we prove a stochastic viability theorem. As a con…

math.PR2012★ 9 cited

Approximation of fractional Brownian motion by martingales

Sergiy Shklyar, Georgiy Shevchenko, Yuliya Mishura +2

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in…