Related papers: Conditioning continuous-time Markov processes by g…
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…
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…
To date, most methods for simulating conditioned diffusions are limited to the Euclidean setting. The conditioned process can be constructed using a change of measure known as Doob's $h$-transform. The specific type of conditioning depends…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
We consider the convergence of a continuous-time Markov chain approximation X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an equidistant lattice and its Q-matrix is chosen to approximate the generator of X. In…
Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble…
Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We connect self-interacting processes, that is, stochastic processes where transitions depend on the time spent by a trajectory in each configuration, to Doob conditioning. In this way we demonstrate that Markov processes with constrained…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…