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We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…
In this note, we prove a version of the Phragmen-Lindelof principle using probabilistic techniques. In particular, we will show that if the p-th moment of the exit time of Brownian motion from a planar domain is finite, then an analytic…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…
The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion $X$. But this method is biased when applied to a stationary version of $X$, in particular an inverse Lamperti transform of $X$, with…
We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an…
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion. The main tool hereby is Doob's formula which gives the probability…
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
Be $X_t$ a random process starting at $x \in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote $P_1(x)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1(x)=x$, equivalent to…
We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dimension higher than two. When at least one Brownian motion…
This paper presents some results on the expected exit time of Brownian motion from simply connected domains in $\CC$. We indicate a way in which Brownian motion sees the identity function and the Koebe function as the smallest and largest…
In this paper we address the question of finding the point which maximizes the $p$-th moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method of excluding parts of the domain from consideration…
This paper determines values of intersection exponents between packs of planar Brownian motions in the half-plane and in the plane that were not derived in our first two papers. For instance, it is proven that the exponent $\xi (3,3)$…
The logarithmic correction for the order of the maximum for two-speed branching Brownian motion changes discontinuously when approaching slopes $\sigma_1^2=\sigma_2^2=1$ which corresponds to standard branching Brownian motion. In this…
It is known from Bramson (1983) that the maximum of branching Brownian motion at time $t$ is asymptotically around an explicit function $m_t$, which involves a first ballistic order and a logarithmic correction. In this paper, we give an…
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi,…
This paper gives an accessible (but still technical) self-contained proof to the fact that the intersection probabilities for planar Brownian motion are given in terms of the intersection exponents, up to a bounded multiplicative error, and…
We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the…
We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass…
Estimates for exit time from an interval of length 2r before a prescribed time T are derived for solutions of a class of stochastic partial differential equations used to characterize two population models: super-Brownian motion and…