In this study, we mainly propose an algorithm to generate correlated random walk converging to fractional Brownian motion, with Hurst parameter, H∈ [1/2,1]. The increments of this random walk are simulated from Bernoulli distribution with proportion p, whose density is constructed using the link between correlation of multivariate Gaussian random variables and correlation of their dichotomized binary variables. We prove that the normalized sum of trajectories of this proposed random walk yields a Gaussian process whose scaling limit is the fractional Brownian motion.
4th International Researchers, Statisticians, Young Statisticians Congress (28 - 30 Nisan 2018)


A generalized correlated random walk approximation to fractional brownian motion
Coşkun, Buket; Vardar Acar, Ceren; Department of Statistics (2018)
The application of fractional Brownian Motion (fBm) has drawn a lot of attention in a large number of areas, ranging from mathematical finance to engineering. The feature of long range dependency limited due to the value of Hurst parameter H ∈ (1/2, 1) makes fBm the desired process for stochastic modelling. The simulation of fBm is also vital for the application in such fields. Hence, the development of an algorithm to simulate an fBm is required in both theoretical and practical aspects of fBm. In this stu...
A generative model for multi class object recognition and detection
Ulusoy, İlkay (2006-01-01)
In this study, a generative type probabilistic model is proposed for object recognition. This model is trained by weakly labelled images and performs classification and detection at the same time. When test on highly challenging data sets, the model performs good for both tasks (classification and detection).
A Probabilistic approach to sparse multi scale phase based stereo
ULUSOY PARNAS, İLKAY; Halıcı, Uğur; HANCOCK, EDWIN (2004-04-30)
In this study, a multi-scale phase based sparse disparity algorithm and a probabilistic model for matching are proposed. The disparity algorithm and the probabilistic approach are verified on various stereo image pairs.
A DRBEM approximation of the Steklov eigenvalue problem
Türk, Önder (Elsevier BV, 2021-01-01)
In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all...
An fMRI segmentation method under markov random fields for brain decoding
Aksan, Emre; Yarman Vural, Fatoş Tunay; Department of Computer Engineering (2015)
In this study, a specially tailored segmentation method for partitioning the fMRI data into a set of "homogenous" regions with respect to a predefined cost function is proposed. The proposed method, referred as f-MRF, employs univariate and multivariate fMRI data analysis techniques under Markov Random Fields to estimate the segments by resolving a mixture density. The univariate approach helps identifying activation pattern of a voxel independently from other voxels. In order to capture local interactions ...
Citation Formats
C. Vardar Acar, “A GENERALIZED CORRELATED RANDOM WALK APPROXIMATION TO FRACTIONAL BROWNIAN MOTION,” presented at the 4th International Researchers, Statisticians, Young Statisticians Congress (28 - 30 Nisan 2018), İzmir, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/78366.