1,721,020 research outputs found
Investigating the distribution of the first-crossing area of a diffusion process with jumps over a threshold
No full textFor a given barrier S and a one-dimensional jump-diffusion process X (t), starting from x < S, we study the probability distribution of the integral (Formula presented.) determined by X (t) till its first-crossing time (Formula presented.) over S. In particular, we show that the Laplace transform and the moments of A (x) S are solutions to certain partial differential-difference equations with outer conditions. The distribution of the minimum of X (t) in [0, πs(x)] is also studied. Thus, we extend the results of a previous paper by the author, concerning the area swept out by X (t) till its firstpassage below zero. Some explicit examples are reported, regarding diffusions with and without jumps
Randomization of a linear boundary in the first-passage problem of Brownian motion.
No full textWe study an inverse first-passage-time problem for Brownian motion XðtÞ, starting from a fixed point x. For t 0, let be SðtÞ 1⁄4 A þ bt a randomly perturbed straight line, where A 1⁄4 Sð0Þ is a random variable, independent of x, such that A x, while b 0 is fixed, and let be F an assigned distribution function. The problem consists in finding the distribution of A such that the first-passage time of X(t) below S(t) has distribution F. The analogous case for fractional Brownian motion with Hurst index H 1⁄4 1, and b 1⁄4 0 is considered. Some explicit examples are reported
Some Remarks on the First-Crossing Area of a Diffusion Process with Jumps over a Constant Barrier.
No full textSome remarks on first-passage times for integrated gauss-markov processes
No full textIt is considered the integrated process X(t) = (formula presented), where Y (t) is a Gauss-Markov process starting from y. The first-passage time (FPT) of X through a constant boundary and the first-exit time of X from an interval (a, b) are investigated, generalizing some results on FPT of integrated Brownian motion
On the excursions of drifted Brownian motion and the successive passage times of Brownian motion.
No full text
On the risk of extinction for a population subject to a random Markov evolution with jumps
No full textWe consider a one-dimensional population whose evolution is described by a jump-diffusion equation and we study the effects of changing the coefficients of the equation on the extinction time, that is the instant at which the population becomes arbitrarily small. It is shown that, under the same diffusion coefficient, if one reduces the drift and the size of jumps, the speed of extinction increases; moreover, the probability of reaching a higher population state than the present one before reaching a lower population size decreases. If the diffusion coefficient is state-independent, the speed of extinction increases with it. Furthermore, if no jumps are allowed (i.e. for a simple-diffusion equation), then under certain conditions on the coefficients of the equation both large and small values of the diffusion coefficient result in a higher extinction risk
One-dimensional reflected diffusions with two boundaries and an inverse first- hitting problem.
No full textWe study an inverse first-hitting problem for a one-dimensional, time-homogeneous
diffusion X(t) reflected between two boundaries a and b, which starts from a random
position η. Let a ≤ S ≤ b be a given threshold, such that P(η [a, S]) = 1, and F
an assigned distribution function. The problem consists of finding the distribution of
η such that the first-hitting time of X to S has distribution F. This is a generalization
of the analogous problem for ordinary diffusions, that is, without reflecting, previously
considered by the author
- …
