相关论文: Stratonovich-type integral with respect to a gener…

The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…

By a classical result of Gauss and Kuzmin, the frequency with which a string $\mathbf{a}=(a_1,\dots,a_n)$ of positive integers appears in the continued fraction expansion of a random real number is given by $\mu_{GK}({I(\mathbf{a})})$,…

Given a $\sigma$-finite infinite measure space $(\Omega,\mu)$, it is shown that any Dunford-Schwartz operator $T:\,\mathcal L^1(\Omega)\to\mathcal L^1(\Omega)$ can be uniquely extended to the space $\mathcal L^1(\Omega)+\mathcal…

Stratified measures on Euclidean space are defined here as convex combinations of rectifiable measures. They are possibly singular with respect to the Lebesgue measure and generalize continuous-discrete mixtures. A stratified measure $\rho$…

We build a setup for path integral quantization through the Faddeev-Jackiw approach, extending it to include Grassmannian degrees of freedom, to be later implemented in a model of generalized electrodynamics that involves fourth-order…

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…

Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…

The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form…

In this note we give a direct proof of the Gaussian integrability of distance function as $\mu e^{\delta d^2(x,x_0)} < \infty$ for some $\delta>0$ provided the Lyapunov condition holds for symmetric diffusion Markov operators, which answers…

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order…

We generalize and extend the stochastic path integral formalism and action principle for continuous quantum measurement introduced in [A. Chantasri, J. Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the optimal…

An innovative theoretical framework for stochastic dynamics based on a decomposition of a stochastic differential equation (SDE) has been developed with an evident advantage in connecting deterministic and stochastic dynamics, as well as…

Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…

In this work we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble…

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…

In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $\rho$-variation for…

In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable L\'evy process and the purely discontinuous Girsanov transform of this process. We also…

A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…

To every log-concave function $f$ one may associate a pair of measures $(\mu_{f},\nu_{f})$ which are the surface area measures of $f$. These are a functional extension of the classical surface area measure of a convex body, and measure how…