Related papers: Properties of Switching Jump Diffusions: Maximum P…
We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…
We study the distribution of the maximal jump of continuous-state branching processes. Several exact expressions and explicit asymptotics of both the local maximal jump and the global maximal jump are obtained. We also compare the…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
In this article, we study the mixing properties of metastable diffusion processes which possess a Gibbs invariant distribution. For systems with multiple stable equilibria, so-called metastable transitions between these equilibria are…
In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…
We deal with the change point problem in ergodic diffusion processes based on high frequency data. Tonaki et al. (2020, 2021) studied the change point problem for the ergodic diffusion process model. However, the change point problem for…
We investigate the multi-chain version of the Chemical Master Equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…