Corpus ID: 221006238

Conditional Distribution of Independent Brownian Motions to Event of Coalescing Paths

@article{Konarovskyi2020ConditionalDO,
  title={Conditional Distribution of Independent Brownian Motions to Event of Coalescing Paths},
  author={Vitalii Konarovskyi and Victor Marx},
  journal={arXiv: Probability},
  year={2020}
}
We consider a family of independent real-valued Brownian motions starting at distinct points and are interested in the description of the conditional distribution of this family to the event that trajectories coalesce, which is of probability zero. We develop a general approach to construct a conditional probability to events of measure zero and apply it first when the above-mentioned family is finite and then when the family is infinite. In both cases, it leads us to the distribution of a… Expand
Representations of the finite-dimensional point densities in Arratia flows with drift
We derive representations for finite-dimensional densities of the point processed associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentialsExpand
Representations of the finite-dimensional point densities in Arratia flows with drift
We derive representations for the finite-dimensional densities of the point processed associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentialsExpand

References

SHOWING 1-10 OF 26 REFERENCES
On asymptotic behavior of the modified Arratia flow
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescingExpand
A new approach for the construction of a Wasserstein diffusion
We propose in this paper a construction of a diffusion process on the Wasserstein space P\_2(R) of probability measures with a second-order moment. This process was introduced in several papers byExpand
Modified Massive Arratia Flow and Wasserstein Diffusion
Extending previous work [arXiv:1408.0628] by the first author we present a variant of the Arratia flow, which consists of a collection of coalescing Brownian motions starting from every point of theExpand
A system of coalescing heavy diffusion particles on the real line
We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proportional to the mass.Expand
On the convergence of sums of independent Banach space valued random variables
The purpose of this paper is to discuss the convergence of sums of independent random variables with values in a separable real Banach space and to apply it to some problems on the convergence of theExpand
The Stochastic Process π
TLDR
This chapter familiarizes the reader with the fact that the conditional distribution of the signal can be viewed as a stochastic process with values in the space of probability measures. Expand
On Infinite System of Diffusing Particles with Coalescing
A system of martingales is constructed that describes a motion of infinite system of diffusing particles sticking together under collision and changing the diffusion coefficient at moment ofExpand
Probability measures on metric spaces
These are some loose notes supporting the first sessions of the seminar Stochastic Evolution Equations organized by Dr. Jan van Neerven at the Delft University of Technology during Winter 2002/2003.Expand
Foundations of modern probability
* Measure Theory-Basic Notions * Measure Theory-Key Results * Processes, Distributions, and Independence * Random Sequences, Series, and Averages * Characteristic Functions and Classical LimitExpand
On convergence determining and separating classes of functions
Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, SkorokhodExpand
...
1
2
3
...