相关论文: On the Absolute-Value Integral of a Brownian Motio…

In this paper we revisit the integral functional of geometric Brownian motion $I_t= \int_0^t e^{-(\mu s +\sigma W_s)}ds$, where $\mu\in\mathbb{R}$, $\sigma > 0$, and $(W_s )_s>0$ is a standard Brownian motion. Specifically, we calculate the…

The joint distribution of a geometric Brownian motion and its time-integral was derived in a seminal paper by Yor (1992) using Lamperti's transformation, leading to explicit solutions in terms of modified Bessel functions. In this paper, we…

We study a Brownian motion with drift in a wedge of angle $\beta$ which is obliquely reflected on each edge along angles $\varepsilon$ and $\delta$. We assume that the classical parameter $\alpha=\frac{\delta+\varepsilon - \pi}{\beta}$ is…

The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairy detailed asymptotic estimates of its density…

This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz.\spacefactor =1000 Brownian motion, bridge, excursion, meander and double meander; for the Brownian…

This paper studies the law of any power of the integral of geometric Brownian motion over any finite time interval. As its main results, two integral representations for this law are derived. This is by enhancing the Laplace transform…

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T), covered by the process in the time interval [0,T]. The Laplace transform…

The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…

Let $\tau$ be the first hitting time of the point 1 by the geometric Brownian motion $X(t)= x \exp(B(t)-2\mu t)$ with drift $\mu \geq 0$ starting from $x>1$. Here $B(t)$ is the Brownian motion starting from 0 with $E^0 B^2(t) = 2t$. We…

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterization of the Laplace transform of their joint law as the unique bounded solution, up…

The density distribution function of the integral of the exponential Brownian motion is determined explicitly in the form of a rapidly convergent series.

We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion $F(\theta,T) = \mathbb{E}[e^{-\theta X_T}]$ with $X_T = \int_0^T e^{\sigma W_s + ( a - \frac12 \sigma^2)s} ds$, which is exact…

This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of…

We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace transform of the stationary distribution…

For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary distribution (when it exists), in terms of Cauchy integrals…

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…

We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the…

In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…

We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary annihilation process, within the Doi-Peliti formalism for…

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + \mu t, t\geq 0,$ where $(B_t)$ is a…