Related papers: Feller Evolution Systems: Generators and Approxima…
We study two equivalent characterizations of the strong Feller property for a Markov process and of the associated sub-Markovian semigroup. One is described in terms of locally uniform absolute continuity, whereas the other uses local…
We show that in the limit of strongly interacting environment a system initially prepared in a Decoherence Free Subspace (DFS) coherently evolves in time, adiabatically following the changes of the DFS. If the reservoir cyclicly evolves in…
Here we give a proof of the existence of c\`{a}dl\`{a}g modification of Markov Processes (on an appropriate space) with Feller semigroup.
In this paper, we study homogenization problem for strong Markov processes on $\R^d$ having infinitesimal generators $$ \sL f(x)=\int_{\R^d}\left(f(x+z)-f(x)-\langle \nabla f(x), z\rangle \I_{\{|z|\le 1\}} \right) k(x,z)\, \Pi (dz) +\langle…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…
Various equivalent conditions for a semigroup or a resolvent generated by a Markov process to be of Feller type are given.
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…
In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\xi)=-i\beta(x)\xi+\gamma(x)|\xi|^{\alpha(x)},$ where $\alpha(x)\in(0,2)$, $\beta(x)\in\R$ and…
We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process…
We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in…
We show that any stochastically monotone Feller semigroup on R can be extended by a consistent family of order-preserving Feller semigroups on the successive powers of R. We exhibit a specific such family, which is uniquely characterized by…
The theory of monotonicity and duality is developed for general one-dimensional Feller processes. Moreover it is shown that local monotonicity conditions (conditions on the L\'evy kernel) are sufficient to prove the well-posedness of the…
Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov…
The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group. In another context, the Thoma cone appears as the set of parameters for totally…
We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection…
In Valiant's model of evolution, a class of representations is evolvable iff a polynomial-time process of random mutations guided by selection converges with high probability to a representation as $\epsilon$-close as desired from the…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…