Related papers: Walsh Spider Diffusions as Time Changed Multi-para…
We consider processes of deterministic motions on $k$ copies of the star-like graph $S_k= K_{1,k}$ with $k$ edges which are perturbed by two stochastic mechanisms: one caused by interfaces located at the graphs' centers, the other…
The aim of this article is to give several results related to Walsh's spider diffusions living on a star-shaped network that have a spinning measure selected from the own local time of the motion at the vertex (cf.[17]). We prove the…
The objective of this article is to prove existence and weak uniqueness of a Walsh spider diffusion process, whose spinning measure and coefficients are allowed to depend on the local time spent at the junction vertex. The methodology is to…
We introduce a class of continuous planar processes, called "semimartingales on rays", and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such planar processes are…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
A diffusion spider is a strong Markov process with continuous paths taking values on a graph with one vertex and a finite number of edges (of infinite length). An example is Walsh's Brownian spider where the process on each edge behaves as…
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional…
A Walsh diffusion on Euclidean space moves along each ray from the origin, as a solution to a stochastic differential equation with certain drift and diffusion coefficients, as long as it stays away from the origin. As it hits the origin,…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face…
Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the…