相关论文: On some transformations between positive self--sim…
Starting from the overdamped Langevin dynamics in $\mathbb{R}^n$, $$ dX_t = -\nabla V(X_t) dt + \sqrt{2 \beta^{-1}} dW_t, $$ we consider a scalar Markov process $\xi_t$ which approximates the dynamics of the first component $X^1_t$. In the…
We show that any $\mathbb{R}^d\setminus\{0\}$-valued self-similar Markov process $X$, with index $\alpha>0$ can be represented as a path transformation of some Markov additive process (MAP) $(\theta,\xi)$ in $S_{d-1}\times\mathbb{R}$. This…
We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…
We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used…
Let $X=(X_t)_{t\geq 0}$ be a known process and $T$ an unknown random time independent of $X$. Our goal is to derive the distribution of $T$ based on an iid sample of $X_T$. Belomestny and Schoenmakers (2015) propose a solution based the…
New algorithms for computing power moments of hitting times and accumulated rewards of hitting type for semi-Markov processes. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations…
This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control…
The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions…
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…
This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative L\'{e}vy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem [Avram, Kyprianou…
We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types repel each other. The interaction of this kind induces an…
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems. For such schemes, a classical stability analysis does not…
In this paper, we consider a class of inhomogeneous semi-Markov processes directly based on intensity processes for marked point processes. We show that this class satisfies the semi-Markov properties defined elsewhere in the literature. We…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…
Conditioning Markov processes to avoid a set is a classical problem that has been studied in many settings. In the present article we study the question if a Levy process can be conditioned to avoid an interval and, if so, the path behavior…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…