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The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal…
We find the exact winding number distribution of Riemann-Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian motion case and it is of…
In this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that…
We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb {Z}$. These scaling limits include the well-known fractional kinetics process, the…
In this paper, we investigate a Brownian motion (BM) with purely time dependent drift and difusion by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We…
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
L\'evy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a particular L\'evy process may be subject to physically…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…
Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this article establishes that the cover time of the Brownian motion…
Quantum fluctuations in time-dependent, harmonically-trapped Bose-Einstein condensates are studied within Bogoliubov theory. An eigenmode expansion of the linear field operators permits the diagonalization of the Bogoliubov-de Gennes…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
In this paper we establish limit theorems for power variations of stochastic processes controlled by fractional Brownian motions with Hurst parameter $H\leq 1/2$. We show that the power variations of such processes can be decomposed into…