相关论文: Stationary distributions for jump processes with i…

We present functional versions of recent results on the univariate distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where $W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x) =\inf\{t>0 :…

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite…

We study the problem of the non-parametric estimation for the density of the stationary distribution of the multivariate stochastic differential equation with jumps (Xt) , when the dimension d is bigger than 3. From the continuous…

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…

Consider the Slepian process $S$ defined by $ S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain…

The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…

In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the…

Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…

We study a one-dimensional Markov modulated random walk with jumps. It is assumed that amplitudes of jumps as well as a chosen velocity regime are random and depend on a time spent by the process at a previous state of the underlying Markov…

With $M(t):=\sup_{s\in[0,t]}A(s)-s$ denoting the running maximum of a fractional Brownian motion $A(\cdot)$ with negative drift, this paper studies the rate of convergence of $\mathbb {P}(M(t)>x)$ to $\mathbb{P}(M>x)$. We define two metrics…

We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate $\gamma$, the (new) velocity of the…

We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…

We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…

We discuss a concept of path-dependent SDE with distributional drift with possible jumps. We interpret it via a suitable martingale problem, for which we provide existence and uniqueness. The corresponding solutions are expected to be…

We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this…

The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…

We consider zero-range processes in ${\mathbb{Z}}^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in ${\mathbb{Z}}^d$ is given by $\lambda_xg(k)p(y-x)$, where $p(\cdot)$ is a probability in…

We study the order statistics of one dimensional branching Brownian motion in which particles either diffuse (with diffusion constant $D$), die (with rate $d$) or split into two particles (with rate $b$). At the critical point $b=d$ which…