Related papers: Quantum Stratonovich Stochastic Calculus and the Q…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
It is widely assumed that there exists a simple transformation from the It\^o interpretation to the one by Stratonovich and back for any stochastic differential equation of applied interest. While this transformation exists under suitable…
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…
We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly…
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
We study power-law behaviors produced from the stochastically dynamical system governed by the well-known two-variable Langevin equations. The stationary solutions of the corresponding Ito's, Stratonovich's and the Zwanzig's (the backward…
In this paper we study the Stratonovich stochastic differential equation $\mathrm{d} X=|X|^{\alpha}\circ\mathrm{d} B$, $\alpha\in(-1,1)$, which has been introduced by Cherstvy et al. [New Journal of Physics 15:083039 (2013)] in the context…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
The article is devoted to the expansion of iterated Stratonovich stochastic integrals of second multiplicity into the double series of products of standard Gaussian random variables. The proof of expansion is based on the application of…
Applying the resolution-scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Ito process driven by the solutions of a Riccati equation.…
We investigate the regularity of the law of Wong-Zakai-type approximations for It\^o stochastic differential equations. These approximations solve random differential equations where the diffusion coefficient is Wick-multiplied by the…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is…
A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and…
A covariant nature of the Langevin equation in Ito calculus is clarified in applying stochastic quantization method to U(N) and SU(N) lattice gauge theories. The stochastic process is expressed in a manifestly general coordinate covariant…
The article is devoted to construction of effective procedures of the mean-square approximation for iterated Stratonovich stochastic integrals of multiplicities 1 to 5. We apply the method of generalized multiple Fourier series for…
In this article, we derive a Stratonovich and Skorohod type change of variables formula for a multidimensional Gaussian process with low H\"older regularity (typically lower than 1/4). To this aim, we combine tools from rough paths theory…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
We consider a class of functions for which the multiple Stratonovich stochastic integral or equivalent iterated Stratonovich stochastic integral with square integrable weights is defined by the orthogonal expansion. The equality of the…
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and…