Related papers: Path probability of stochastic motion: A functiona…
Attempts to find a quantum-to-classical correspondence in a classically forbidden region leads to non-physical paths, involving, for example, complex time or spatial coordinates. Here, we identify genuine quasi-classical paths for tunneling…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.
This paper is devoted to the price-storage dynamics in natural gas markets. A novel stochastic path-dependent volatility model is introduced with path-dependence in both price volatility and storage increments. Model calibrations are…
We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of…
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…
Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…
Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…
Probabilistic approach to the description of translational motion of macrobodies indicates the emergence of additional order effects oriented in the direction of motion of the body
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to…
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on…