4 papers · 1 filter
Strong uniqueness for fractional stochastic differential equations with sign drift
Ercan Sönmez, Yuliya Mishura
Establishing pathwise uniqueness for stochastic differential equations driven by fractional Brownian motion with Hurst parameter remains challenging, particularly for disco…
Hadamard fractional Brownian motion: path properties and Wiener integration
Luisa Beghin, Alessandro De Gregorio, Yuliya Mishura
The so-called Hadamard fractional Brownian motion, as defined in Beghin et al. (2025) by means of Hadamard fractional operators, is a Gaussian process which shares some properties…
Discrete-time weak approximation of a Black-Scholes model with drift and volatility Markov switching
Vitaliy Golomoziy, Kamil Kladivko, Yuliya Mishura
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uni…
Probabilistic Cauchy Functional Equations
Ehsan Azmoodeh, Noah Beelders, Yuliya Mishura
In this short note, we introduce probabilistic Cauchy functional equations, specifically, functional equations of the following form: $$ f(X_1 + X_2) \stackrel{d}{=} f(X_1) + f(X_2…