Related papers: Path Integrals and Perturbation Theory for Stochas…
We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes…
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…
We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose…
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…
Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then…
We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multi-variate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to…
Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and…