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Modern Stochastics Theory and Applications Volume 2020 Issue 2006

Subject Areas: Statistics, Probability and Uncertainty
ISSN: 2351-6046
SJR: 4

Open Access

Journal Article

A pure-jump mean-reverting short rate model

Hess, Markus

2020 Mathematics

doi:10.15559/20-VMSTA152

Abstract: A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond prices possess affine representations. Also the...
Open Access

Journal Article

Single jump filtrations and local martingales

Gushchin, Alexander A.

2020 Mathematics

doi:10.15559/20-VMSTA153

Abstract: A single jump filtration $({\mathscr{F}}_t)_{t\in \mathbb{R}_+}$ generated by a random variable $\gamma$ with values in $\overline{\mathbb{R}}_+$ on a probability space $(\Omega ,{\mathscr{F}},\mathsf{P})$ is defined as follows: a set $A\in {\mathscr{F}}$ belongs to ${\mathscr{F}}_t$ if...
Open Access

Journal Article

Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

Marzougue, Mohamed; Sagna, Yaya

2020 Mathematics

doi:10.15559/20-VMSTA155

Abstract: In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of...
Open Access

Journal Article

Distance from fractional Brownian motion with associated Hurst index $0<H<1/2$ to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent

Banna, Oksana; Buryak, Filipp; Mishura, Yuliya

2020 Mathematics

doi:10.15559/20-VMSTA156

Abstract: We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form $\int _0^ts^{\gamma}dW_s$, where $W$ is a Wiener process, $\gamma >0$.
Open Access

Journal Article

Prediction in polynomial errors-in-variables models

Kukush, Alexander; Senko, Ivan

2020 Mathematics

doi:10.15559/20-VMSTA154

Abstract: A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors...

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