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We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
In this paper, we develop a new general approach to the existence and uniqueness theory of infinite dimensional stochastic equations of the form dX+A(t)Xdt = XdW in (0;T)xH, where A(t) is a nonlinear monotone and demicontinuous operator…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and…
We deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to the heat-type equation where the time derivative is…
This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…
We introduce the multivariate Log S-fBM model (mLog S-fBM), extending the univariate framework proposed by Wu \textit{et al.} to the multidimensional setting. We define the multidimensional Stationary fractional Brownian motion (mS-fBM),…
We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…
Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the fractional Bessel process. It\^{o}'s formula for…
The $d$-dimensional fractional Brownian motion (FBM for short) $B_t=((B_t^{(1)},...,B_t^{(d)}),t\in\mathbb{R})$ with Hurst exponent $\alpha$, $\alpha\in(0,1)$, is a $d$-dimensional centered, self-similar Gaussian process with covariance…
We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed…
In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…
The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional…