Related papers: On Berman functions
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these…
We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…
We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. The mean-square rate of convergence of Euler approximations of solution to this…
We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we…
Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance \[ R^{(H,K)}(s,t)= 2^{-K} \left( \left(|s|^{2H}+|t|^{2H} \right)^{K}-|t-s|^{2HK}\right), \qquad s,t\in R. \] We study the existence of bfBm for a given pair…
In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a…
We prove that the Fourier dimension of the graph of fractional Brownian motion with Hurst index greater than $1/2$ is almost surely 1. This extends the result of Fraser and Sahlsten (2018) for the Brownian motion and confirms part of the…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin-Merzbach (2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is proved to statisfy a strenghtened definition of increment…
It is discussed the limitations of the widely used markovian approximation applied to model the turbulent refractive index in lightwave propagation. It is well-known the index is a passive scalar field. Thus, the actual knowledge about…
In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of…
We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is…
A recently proposed alternative to multifractional Brownian motion (mBm) with random Hurst exponent is studied, which we refer to as It\^o-mBm. It is shown that It\^o-mBm is locally self-similar. In contrast to mBm, its pathwise regularity…
Be $X_t$ a random process starting at $x \in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to…
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…
This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral…
A variational representation for functionals of G-Brownian motion is established by a finite-dimensional approximate technique. As an application of the variational representation, we obtain a large deviation principle for stochastic flows…
We consider a Brownian motion (BM) $x(\tau)$ and its maximal value $x_{\max} = \max_{0 \leq \tau \leq t} x(\tau)$ on a fixed time interval $[0,t]$. We study functionals of the maximum of the BM, of the form ${\cal O}_{\max}(t)=\int_0^t\,…
We investigate numerical approximations for the stochastic Burgers equation driven by an additive cylindrical fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$. To discretize the continuous problem in space, a…