相关论文: Pathwise Taylor Expansions for Random Fields on Mu…

Series expansions in the chemical potential mu are studied for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified…

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…

Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…

We prove simultaneous Universal Approximation of a certain type of Pade Approximants and of Taylor series with the same indexes. This is a generic phenomenon in the space of holomorphic functions in any simply connected domain, as well as…

Thimble regularisation is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the…

We investigate stochastic parabolic evolution equations with time-dependent random generators and locally Lipschitz continuous drift terms. Using pathwise mild solutions, we construct an infinite-dimensional stationary Ornstein-Uhlenbeck…

We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…

We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet…

We study an evolutionary $p$-Laplace problem whose potential is subject to a translation in time. Provided the trajectory along which the potential is translated admits a sufficiently regular local time, we establish existence of solutions…

We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution…

We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all…

We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the…

We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of $p$-th variation along a sequence of time…

A Lagrangian method is used to show that the power-law with a -7/2 exponent in the negative tail of the pdf of the velocity gradient and of velocity increments, predicted by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78, 1904) for…

In some recent articles we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials. In this generalized SUSY QM partnership, the DBT are built on the excited states…

We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [Ann Appl Probab. 27:6 (2017) 1-37] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff…

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a…

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.

The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an It\^{o} formula like the solution…

We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…