相关论文: Construction of the Paths of Brownian Motions on S…
Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of single vertex graphs are given.
A pathwise construction of discontinuous Brownian motions on metric graphs is given for every possible set of non-local Feller-Wentzell boundary conditions. This construction is achieved by locally decomposing the metric graphs into star…
Brownian motions on a metric graph are defined. Their generators are characterized as Laplace operators subject to Wentzell boundary at every vertex. Conversely, given a set of Wentzell boundary conditions at the vertices of a metric graph,…
Brownian motions on star graphs in the sense of It\^o-McKean, that is, Walsh processes admitting a generalized boundary behavior including stickiness and jumps and having an angular distribution with finite support, are examined. Their…
The construction of the paths of all possible Brownian motions (in the sense of Knight) on a half line or a finite interval is reviewed.
We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.
Consider a metric graph G with set of vertices V. Assume that for every vertex in V one is given a Wentzell boundary condition. It is shown how one can construct the paths of a Brownian motion on G such that its generator - viewed as an…
A classification for Brownian motions on metric graphs, that is, right continuous strong Markov processes which behave like a one-dimensional Brownian motion on the edges and feature effects like Walsh skewness, stickiness and jumps at the…
We provide a detailed description of all possible Feller processes on infinite} star graphs with finite number of edges, processes that while away from the graph's center behave like a one-dimensional Brownian motion. The description can be…
We prove that minimal graphs (other than planes) are parabolic in the sense that any bounded harmonic function is determined by its boundary values. The proof relies on using the coupling introduced in the author's earlier paper "A…
Brownian motions on a metric graph are defined, their Feller property is proved, and their generators are characterized. This yields a version of Feller's theorem for metric graphs.
This paper is concerned with the construction of several stochastic processes in a star graph, that is a non-euclidean structure where some features of the classical modelling fail. We propose a model for trapping phenomena with…
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a…
Weconsider Burgers equation on metric graphs for simplest topologies such as star, loops, and tree graphs. Exact traveling wave solutions are obtained for the vertex boundary conditions providing mass conservation and continuity of the…
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…
The signature of Brownian motion in $\mathbb{R}^{d}$ over a running time interval $[0,T]$ is the collection of all iterated Stratonovich path integrals along the Brownian motion. We show that, in dimension $d\geq 2$, almost all Brownian…
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral…