4 citations · 15 across the 14 of their papers we have counts for
14 papers
Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets
Rachid Belfadli, Youssef Ouknine, Ercan Sönmez
In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fract…
Intersection probabilities for flats in hyperbolic space
Ercan Sönmez, Panagiotis Spanos, Christoph Thäle
Consider the -dimensional hyperbolic space of constant curvature and fix a point playing the role of an origin. Let be a uniform random $…
On the distances within cliques in a soft random geometric graph
Ercan Sönmez, Clara Stegehuis
We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away point…
On the existence and regularity of local times
Tommi Sottinen, Ercan Sönmez, Lauri Viitasaari
We study the existence and regularity of local times for general -dimensional stochastic processes. We give a general condition for their existence and regularity properties. To…
The longest edge of the one-dimensional soft random geometric graph with boundaries
Arnaud Rousselle, Ercan Sönmez
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynom…
Persistence probabilities of mixed FBM and other mixed processes
Frank Aurzada, Martin Kilian, Ercan Sönmez
We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further…
The longest edge in discrete and continuous long-range percolation
Arnaud Rousselle, Ercan Sönmez
We consider the random connection model in which an edge between two Poisson points at distance is present with probability . We conduct an extreme value analysis on this…
On mixed fractional SDEs with discontinuous drift coefficient
Ercan Sönmez
We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional…
Graph distances of continuum long-range percolation
Ercan Sönmez
We consider a version of continuum long-range percolation on finite boxes of in which the vertex set is given by the points of a Poisson point process and each pair…
The random walk on the random connection model
Ercan Sönmez, Arnaud Rousselle
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices and are connected with probability that asympt…
Max-linear models in random environment
Claudia Klüppelberg, Ercan Sönmez
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation…
On the carrying dimension of occupation measures for self-affine random fields
Peter Kern, Ercan Sönmez
Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for…
Fractal behavior of multivariate operator-self-similar stable random fields
Ercan Sönmez
We investigate the sample path regularity of multivariate operator-self-similar stable random fields with values in given by a harmonizable representation. Such fiel…
Sample path properties of generalized random sheets with operator scaling
Ercan Sönmez
We consider operator scaling -stable random sheets, which were introduced in [12]. The idea behind such fields is to combine the properties of operator scaling -stable random…