Related papers: Complex paths for real stochastic processes
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
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…
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…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
The It\^o formula, also known as the change-of-variables formula, is a cornerstone of It\^o stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. Since…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
The It\^o formula, originated by K. It\^o, is focus on the stochastic calculus, where many stochastic processes can be placed under the framework of rough paths. In rough path theory, It\^o formulas have been proved for rough paths with…
Given a multi-dimensional It\^{o} process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the It\^{o} process at each fixed time.…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
We study the path-integral formalism in the imaginary-time to show its validity in a case with a metastable ground state. The well-known method based on the bounce solution leads to the imaginary part of the energy even for a state that is…
The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from…
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…
We review the analytical methods of solving the stochastic equations for barrier-type dynamical behavior in plasma systems. The path-integral approach is examined as a particularly efficient method of determination of the statistical…