Researcher:
Karakuş, Abdullah Harun

Profile Picture
ORCID

Job Title

Master Student

First Name

Abdullah Harun

Last Name

Karakuş

Name

Name Variants

Karakuş, Abdullah Harun

Email Address

Birth Date

Filters

20183

Advanced Search

Filter by

Settings

Researcher Of Publications: search.filters.isAuthorOfPublication.7f32ef3f-d395-4c2e-963d-5bc7167f48e5

Search Results

Now showing 1 - 3 of 3
  • Placeholder
    PublicationMetadata only
    Correlated coalescing Brownian flows on R and the circle
    (IMPA - Instituto de Matemática Pura e Aplicada, 2018) Hajri, Hatem; Department of Mathematics; N/A; Çağlar, Mine; Karakuş, Abdullah Harun; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 105131; N/A
    We consider a stochastic differential equation on the real line which is driven by two correlated Brownian motions B+ and B- respectively on the positive half line and the negative half line. We assume |d〈B+,B-〉t| ≤ ρ dt with ρ ∈ [0, 1). We prove it has a unique flow solution. Then, we generalize this flow to a flow on the circle, which represents an oriented graph with two edges and two vertices. We prove that both flows are coalescing. Coalescence leads to the study of a correlated reflected Brownian motion on the quadrant. Moreover, we find the distribution of the hitting time to the origin of a reflected Brownian motion. This has implications for the effect of the correlation coefficient ρ on the coalescence time of our flows.
  • Thumbnail Image
    PublicationOpen Access
    Correlated coalescing Brownian flows on R and the circle
    (The International Marine Purchasing Association (IMPA), 2018) Hajri, Hatem; Department of Mathematics; Çağlar, Mine; Karakuş, Abdullah Harun; Faculty Member; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 105131; N/A
    We consider a stochastic differential equation on the real line which is driven by two correlated Brownian motions B+ and B- respectively on the positive half line and the negative half line. We assume vertical bar d < B+, B->(t)vertical bar <= rho dt with rho is an element of [0, 1). We prove it has a unique flow solution. Then, we generalize this flow to a flow on the circle, which represents an oriented graph with two edges and two vertices. We prove that both flows are coalescing. Coalescence leads to the study of a correlated reflected Brownian motion on the quadrant. Moreover, we find the distribution of the hitting time to the origin of a reflected Brownian motion. This has implications for the effect of the correlation coefficient rho on the coalescence time of our flows.
  • Thumbnail Image
    PublicationOpen Access
    Planar Brownian flows with rank-based characteristics
    (American Institute of Physics (AIP) Publishing, 2018) Karatzas, Ioannis; Department of Mathematics; Çağlar, Mine; Karakuş, Abdullah Harun; Faculty Member; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 105131; N/A
    We study a stochastic differential equation with rank-based characteristics on the plane. We find its flow solutions and characterize coalescence.