Taylor, First passage times and sojourn times for Brownian
motion in space and the exact Hausdorff measure of the sample path, Trans.
The population balance equation describing irreversible Brownian
coagulation with continuous monovariable can be written as follows :
In this paper, we will mainly study the pricing problem of a class European vulnerable option under a mixed fractional Brownian
Although he did not exploit all richness of his model, Langevin obtained in the long-time regime Einstein's result, namely, by <[x.sup.2]> = 2([k.sub.B]T/6[pi]a[mu])t, where a is the radius of particle, [mu] is fluid viscosity, T is temperature, and [k.sub.B] is the Boltzmann's constant, hence bridging Brownian
motion, random walk, and diffusion, a view soon quantified experimentally by Perrin .
D increased with temperature increasing, and then Brownian
motion of particles increased.
"I'm not a big fan of Brownian
Motion or statistical distributions, you probably gather.
To address this issue for the Heston model, a natural idea is to replace the two Brownian
motions by fractional Brownian
motions (FBM), see [5, 21].
The Gaussian nature of the motion and the length of the step are compelling indications that the myosin head walks or slides along the actin monomer, that is to say myosin transverses actin by Brownian
motion (34) (Fig.
Here, the parent process X(s) is an integrated Brownian
motion, defined by
The influence of nonuniform heat source/sink with the Brownian
motion and thermophoresis on non-Newtonian nanofluids over a cone was illustrated by Raju et al.
The study of optimal stopping time for stochastic processes, especially geometric Brownian
motion, has a long history in finance literature.
In the work  the authors mainly work with a discrete time scale; in  the authors introduce an extension of a function and define the stochastic as well as deterministic integrals as the usual integrals for the extended function; in  the authors make use of their results on the quadratic variation of a Brownian
motion () on time scales and, based on this, they define the stochastic integral via a generalized version of the Ito isometry; in  the authors introduce the so-called [nabla]-stochastic integral via the backward jump operator and they also derive an Ito formula based on this definition of the stochastic integral.