4 papers
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…
Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter
Volodymyr Braiman, Anatoliy Malyarenko, Yuliya Mishura +1
We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More prec…