Related papers: Fractional Cox--Ingersoll--Ross process with non-z…

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…

This paper develops an It\^o-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons' rough path framework. This approach is designed to fill…

In previous works, Bardina and Rovira (2023) constructed a family of processes that converge strongly towards Brownian motion, defined from renewal processes, are constructed. In this paper we prove that some of these processes can be…

This paper considers maximum likelihood inference for a functional marked point process - the stochastic growth-interaction process - which is an extension of the spatio-temporal growth-interaction process to the stochastic mark setting. As…

This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…

Bifractional Brownian motion on $\mathbb{R}_+$ is a two parameter centered Gaussian process with covariance function: \[ R_{H,K} (t,s)=\frac 1{2^K}\left(\left(t^{2H}+s^{2H}\right)^K-\ |{t-s}\ |^{2HK}\right), \qquad s,t\ge 0. \] This process…

Let $B_H=\{B_H(t):t\in\mathbb R\}$ be a fractional Brownian motion with Hurst parameter $H\in(0,1)$. For the stationary storage process $Q_{B_H}(t)=\sup_{-\infty<s\le t}(B_H(t)-B_H(s)-(t-s))$, $t\ge0$, we provide a tractable criterion for…

We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index $H \textgreater{} 1/ 2$. When $H$ is smaller than or equal to $3…

We study the large deviations for Cox-Ingersoll-Ross (CIR) processes with small noise and state-dependent fast switching via associated Hamilton-Jacobi equations. As the separation of time scales, when the noise goes to $0$ and the rate of…

In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…

If we compose a smooth function g with fractional Brownian motion B with Hurst index H > 1/2, then the resulting change of variables formula [or It/^o- formula] has the same form as if fractional Brownian motion would be a continuous…

In this paper, we study the asymptotic behavior of supremum distribution of some classes of iterated stochastic processes $\{X(Y(t)) : t \in [0, \infty)\}$, where $\{X(t) : t \in \mathbb{R} \}$ is a centered Gaussian process and $\{Y(t): t…

We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an…

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the…

We are interested in the quasi-stationarity of the time-inhomogeneous Markov process X t = B t (t + 1) $\kappa$ where (B t) t$\ge$0 is a one-dimensional Brownian motion and $\kappa$ $\in$ (0, $\infty$). We first show that the law of X t…

In this paper, we investigate the stochastic counterpart of the generalized Wright analysis introduced in Beghin et al.~ in Integral Equations and Operator Theory, {\bf 97}, 2025. We define a new class of non-Gaussian and non-Markovian…

The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental…

We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, with respect to fractional Brownian motion with Hurst parameter $H \in (1/2,1)$, for a large class of convex functions $f$ is considered. In…