Related papers: Occurence Probabilities of Stochastic Paths
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
The calculation of the decay rate of a metastable state in the path-integral formulation of stochastic processes is revisited. Previous derivations of this rate were achieved at the cost of a step that is difficult to justify…
We present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The approach is based on the chaos representation property and…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linear systems and matrix equations for generating functions…
The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that $n_1$, $n_2$, $n_3$, . . . distinct sites are visited at times $t_1$, $t_2$, $t_3$,…
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link…