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math.PR2025
Tanaka formula for SDEs driven by fractional Brownian motion
Tommi Sottinen, Ercan Sönmez, Lauri Viitasaari
We derive a Tanaka-type formula for the solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (fBm) with Hurst parameter . Whil…
math.PR2024
Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands
Kostiantyn Ralchenko, Foad Shokrollahi, Tommi Sottinen
We establish the rate of convergence in the -norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motio…
math.PR2024
On the existence and regularity of local times
Tommi Sottinen, Ercan Sönmez, Lauri Viitasaari
We study the existence and regularity of local times for general -dimensional stochastic processes. We give a general condition for their existence and regularity properties. To…