Search results for "Markov process"
showing 10 items of 147 documents
The Concept of Duality and Applications to Markov Processes Arising in Neutral Population Genetics Models
1999
One possible and widely used definition of the duality of Markov processes employs functions H relating one process to another in a certain way. For given processes X and Y the space U of all such functions H, called the duality space of X and Y, is studied in this paper. The algebraic structure of U is closely related to the eigenvalues and eigenvectors of the transition matrices of X and Y. Often as for example in physics (interacting particle systems) and in biology (population genetics models) dual processes arise naturally by looking forwards and backwards in time. In particular, time-reversible Markov processes are self-dual. In this paper, results on the duality space are presented f…
Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths
2009
The dynamics of two interacting spins coupled to separate bosonic baths is studied. An analytical solution in Born approximation for arbitrary spectral density functions of the bosonic environments is found. It is shown that in the non-Markovian cases concurrence "lives" longer or reaches greater values.
A Bayesian analysis of a queueing system with unlimited service
1997
Abstract A queueing system occurs when “customers” arrive at some facility requiring a certain type of “service” provided by the “servers”. Both the arrival pattern and the service requirements are usually taken to be random. If all the servers are busy when customers arrive, they usually wait in line to get served. Queues possess a number of mathematical challenges and have been mainly approached from a probability point of view, and statistical analysis are very scarce. In this paper we present a Bayesian analysis of a Markovian queue in which customers are immediately served upon arrival, and hence no waiting lines form. Emergency and self-service facilities provide many examples. Techni…
Non-Markovianity and Coherence of a Moving Qubit inside a Leaky Cavity
2017
Non-Markovian features of a system evolution, stemming from memory effects, may be utilized to transfer, storage, and revive basic quantum properties of the system states. It is well known that an atom qubit undergoes non-Markovian dynamics in high quality cavities. We here consider the qubit-cavity interaction in the case when the qubit is in motion inside a leaky cavity. We show that, owing to the inhibition of the decay rate, the coherence of the traveling qubit remains closer to its initial value as time goes by compared to that of a qubit at rest. We also demonstrate that quantum coherence is preserved more efficiently for larger qubit velocities. This is true independently of the evol…
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Donsker-Type Theorem for BSDEs: Rate of Convergence
2019
In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence. peerReviewed
Contributed discussion on article by Pratola
2016
The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
Statistics of residence time for Lévy flights in unstable parabolic potentials
2020
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
Stochastic Control Problems
2003
The general theory of stochastic processes originated in the fundamental works of A. N. Kolmogorov and A. Ya. Khincin at the beginning of the 1930s. Kolmogorov, 1938 gave a systematic and rigorous construction of the theory of stochastic processes without aftereffects or, as it is customary to say nowadays, Markov processes. In a number of works, Khincin created the principles of the theory of so-called stationary processes.