相关论文: Time since maximum of Brownian motion and asymmetr…

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point…

For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…

We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…

We study the extremes of variable speed branching Brownian motion (BBM) where the time-dependent "speed functions", which describe the time-inhomogeneous variance, converge to the identity function. We consider general speed functions lying…

Let $X=(X_t)_{t\ge0}$ be a transient diffusion process in $(0,\infty)$ with the diffusion coefficient $\sigma>0$ and the scale function $L$ such that $X_t\rightarrow\infty$ as $t\rightarrow \infty$, let $I_t$ denote its running minimum for…

We study the distribution of the exponential functional $I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t$, where $\xi$ and $\eta$ are independent L\'evy processes. In the general setting using the theories of Markov processes and…

We present a novel theoretical result on estimation of local time and occupation time measure of an {\alpha}-stable L\'evy process with {\alpha} in (1, 2). Our approach is based upon computing the conditional expectation of the desired…

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process,…

We derive a Ray-Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken…

The conditional density of Brownian motion is considered given the max, B(t|\max), as well as those with additional information: B(t|close, max), B(t|close, max, min) and B(t|max, min) where the close is the final value: B(t=1)=c and t in…

This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

Among Markovian processes, the hallmark of L\'evy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that L\'evy laws, as well as Gaussians, can also be the limit distributions of processes with long range memory that…

Let be $(X_t, t\geq 0)$ be a L\'evy process which is the sum of a Brownian motion with drift and a compound Poisson process. We consider the first passage time $\tau_x$ at a fixed level $x>0$ by $(X_t, t\geq 0)$ and $K_x:= X_{\tau_x}-x$ the…

We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…

Given a spectrally negative L\'evy process $X$ drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the $L^p$ distance ($p>1$) with $g$, the last time $X$ is…

A L\'evy process is said to creep through a curve if, at its first passage time across this curve, the process reaches it with positive probability. We first study this property for bivariate subordinators. Given the graph…

We study the ballistic L\'evy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a `light' cone $-v_0…

Let $^{(r,s)}X_t$ be the L\'evy process $X_t$ with the $r$ largest jumps and $s$ smallest jumps up till time $t$ deleted and let $^{(r)}\tilde X_t$ be $X_t$ with the $r$ largest jumps in modulus up till time $t$ deleted. We show that…