Related papers: p-variation of strong Markov processes

An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…

We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…

Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local…

In this paper we consider an additive functional of an observable $V(x)$ of a Markov jump process. We assume that the law of the expected jump time $t(x)$ under the invariant probability measure $\pi$ of the skeleton chain belongs to the…

There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process…

We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…

The paper is devoted to the existence of integral functionals $\int_0^\infty f(X(t))\,{\mathrm{d}t}$ for several classes of processes in $\mathbb{R}$ with $d\ge 3$. Some examples such as Brownian motion, fractional Brownian motion, compound…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

Consider a Markov chain $(X_i)_{i\ge0}$ with invariant measure $\mu$ that admits the representation $X_{i+1}=\Phi(X_i,U_i)$, where $(U_i)_{i\ge0}$ are i.i.d. random variables and $\Phi$ is a measurable map. We introduce a tangent-decoupled…

Let $(T,d)$ be a metric space and $\phi:\mathbb{R}_+\to \mathbb{R}$ an increasing, convex function with $\phi(0)=0$. We prove that if $m$ is a probability measure $m$ on $T$ which is majorizing with respect to $d,\phi$, that is,…

The main contribution of this paper is a strong converse result for $K$-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II…

Given an increasing process $(A_t)_{t\geq 0}$, we characterize the right-continuous non-decreasing functions $f: \R_+\to \R_+$ that map $A$ to a pure-jump process. As an example of application, we show for instance that functions with…

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 study asymptotic properties of the following Markov system of $N \geq 3$ points in~$[0,1]$. At each time step, the point farthest from the current centre of mass, multiplied by a constant $p>0$, is removed and replaced by an independent…

Let $\langle x\rangle^{\alpha}=(\max\{|x|_{p},p^r\})^{\alpha}$ and $H^{\alpha}\varphi=\mathcal{F}^{-1}[(\langle \xi\rangle^{\alpha} -p^{r\alpha})\mathcal{F}\varphi]$, in this article we study the Markov process associated to this operator…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

Let $X$ be the number of $k$-term arithmetic progressions contained in the $p$-biased random subset of the first $N$ positive integers. We give asymptotically sharp estimates on the logarithmic upper-tail probability $\log \Pr(X \ge E[X] +…

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

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…

We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition…