Related papers: Small ball probabilities and large deviations for …
We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the…
We study the problem of when a Brownian motion in the unit ball has a positive probability of avoiding a countable collection of spherical obstacles. We give a necessary and sufficient integral condition for such a collection to be…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at $-\infty$. We show that these processes do not have to have…
We study the density of the support of a dyadic $d$-dimensional branching Brownian motion (BBM) in subcritical balls in $\mathbb{R}^d$. Using elementary geometric arguments and an extension of a previous result on the probability of absence…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
We study the norm of the two-dimensional Brownian motion conditioned to stay outside the unit disk at all times. By conditioning the process is changed from barely recurrent to slightly transient. We obtain sharp results on the rate of…
The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of the Brownian motion on $\mathsf{GL}(N;\mathbb{C}),$ in the sense of $\ast $-distributions. The natural candidate for the large-$N$ limit of the empirical distribution…
We study a spatial branching model, where the underlying motion is $d$-dimensional ($d\ge1$) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result…
We study a $d$-dimensional branching Brownian motion inside subdiffusively expanding balls, where the boundary of the ball is deactivating in the sense that once a particle hits the moving boundary, it is instantly deactivated but is…
We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…
In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
We consider a model of Brownian motion on a bounded open interval with instantaneous jumps. The jumps occur at a spatially dependent rate given by a positive parameter times a continuous function positive on the interval and vanishing on…
In this note we prove that the probability measures generated by two generalized grey Brownian motions with different parameters are singular with respect to each other. This result can be interpreted as an extension of the Feldman-H\'ajek…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…