According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus ...the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order.
Brownian motion with linear drift on positive half-line and killed elastically at zero is considered. A goal is to get a result that allows us to calculate the distributions of integral functionals ...with respect to spatial variable of local time of such a process. The explicit form of the distribution of the supremum with respect to spatial variable of local time is calculated for Brownian motion with linear drift reflecting at zero.
A skew Brownian motion with piecewise constant drift is considered. This diffusion includes a skew Brownian motion with linear drift with equal constants and it turns into a skew Brownian motion with ...alternating drift with opposite sign constants. We are interested in the result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of a skew Brownian motion with discontinuous drift.
The paper deals with the results that allow one to calculate the joint distributions of functionals of diffusions with switchings that occur at random time moments depending on the diffusion ...trajectory. Standard switchings from one set of diffusion coefficients to another occur at random time moments corresponding to the jump moments of a Poisson process independent of the initial diffusions. More general nonstandard switching occurs when the integral functional of the trajectory reaches the value equal to an exponentially distributed variable. With unit integrand such switching becomes standard.
Diffusion with piecewise constant drift and diffusion coefficient 1 is considered. Such a process is called the Brownian motion with discontinuous drift. At equal constants, this diffusion includes a ...Brownian motion with linear drift and at constants with opposite sign, it turns into a Brownian motion with variable drift. The goal of the paper is to get a result that allows to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of Brownian motion with discontinuous drift. The explicit form of the distribution of the supremum with respect to spatial variable of the local time of Brownian motion with discontinuous drift is calculated.
The standard switching from one set of diffusion coefficients to another one occurs at random times corresponding to the moments of jumps of a Poisson process independent of the initial diffusion. ...The paper deals with the process of Brownian motion with variance taking one of two values by the switching depending on trajectories of the process. The most attractive from the computational point of view is the moment inverse to local time.
The paper deals with the limit behavior of a compound Poisson process with switching between a finite number of sequences of i.i.d. random variables. The switching is provided by Bernoulli’s random ...variables. Under suitable normalization, the limit process is a Brownian motion with switching variance.
The paper deals with limit behavior of a compound Poisson process with switching and dominated summands. The switching is provided by Bernulli’s random variables and a Markov chain. Under suitable ...normalization the limit process is a Brownian motion with switching variance and jumps.
The paper deals with methods for calculating distributions of functionals of switching diffusions with jumps. The switching between two collections of diffusion coefficients occurs at the Poisson ...time moments which are independent of the initial diffusions. At the same moments, the diffusion can have jumps. The process controlling the switching is determined by a Markov chain.
The paper deals with the limit behavior of a compound Poisson process with switching. The switching is provided by Bernoulli’s random variables. Under a suitable normalization, the limit process is a ...Brownian motion with switching variance.
