Related papers: A note on fast times of Brownian motion with varia…

We compute the Hausdorff dimension of the image X(E) of a non random Borel set E $\subset$ [0, 1], where X is a L\'evy multistable process in R. This extends the case where X is a classical stable L\'evy process by letting the stability…

Denote by $H(t)=(H_1(t),...,H_N(t))$ a function in $t\in{\mathbb{R}}_+^N$ with values in $(0,1)^N$. Let $\{B^{H(t)}(t)\}=\{B^{H(t)}(t),t\in{\mathbb{R}}^N_+\}$ be an $(N,d)$-multifractional Brownian sheet (mfBs) with Hurst functional $H(t)$.…

In a series of recent preprints, we have proven that with probability one the Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3, confirming a conjecture by Mandelbrot. It is also shown that the Hausdorff dimension…

Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…

An additive process is a stochastic process with independent increments and that is continuous in probability. In this paper, we study the almost sure Hausdorff and Fourier dimension of the graph of continuous additive additive processes…

This paper studies time changes of Brownian motions by positive continuous additive functionals. Under a certain regularity condition on the associated Revuz measures, we prove that the resolvents of the time-changed Brownian motions are…

We prove uniform Hausdorff and packing dimension results for the inverse images of a large class of real-valued symmetric L\'evy processes. Our main result for the Hausdorff dimension extends that of Kaufman (1985) for Brownian motion and…

In this paper, high-order moment, even exponential moment, estimates are established for the H\"older norm of solutions to stochastic differential equations driven by fractional Brownian motion whose drifts are measurable and have linear…

We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also computed. We use the result to describe the transitional…

It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any alpha<1/2 there are alpha-H\"older continuous functions f for which the process B-f has isolated zeros with…

Let $B =\{ B_t \, : \, t \geq 0 \}$ be a real-valued fractional Brownian motion of index $H \in (0,1)$. We prove that the macroscopic Hausdorff dimension of the level sets $\mathcal{L}_x = \left\{ t \in \mathbb{R}_+ \, : \, B_t=x \right\}$…

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in [5]. In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation).…

We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.

A Brownian spatial tree is defined to be a pair $(\mathcal{T},\phi)$, where $\mathcal{T}$ is the rooted real tree naturally associated with a Brownian excursion and $\phi$ is a random continuous function from $\mathcal{T}$ into…

Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck…

We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…

Let X^{1}, X^{2} be two independent (two-sided) fractional Brownian motions having the same Hurst parameter H in (0,1), and let Y be a standard (one-sided) Brownian motion independent of (X^{1},X^{2}). In dimension 2, fractional Brownian…

In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the…

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related…

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…