Search results for "Bessel process"
showing 5 items of 5 documents
Bounds for Bessel functions
1989
We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.
On first exit times and their means for Brownian bridges
2017
For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), \,\, h>0,$ behaves as $O(h^2)$ when $h \downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.
Quantum extensions of semigroups generated by Bessel processes
1996
We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Stochastic acceleration in generalized squared Bessel processes
2015
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.