相关论文: A Feynman-Kac Formula for Anticommuting Brownian M…
An anticommuting analogue of Brownian motion, corresponding to fermionic quantum mechanics, is developed, and combined with classical Brownian motion to give a generalised Feynman-Kac-It\^o formula for paths in geometric supermanifolds.…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles…
(Replacement because mailer changed `hat' for supercript into something weird. The macro `\sp' has been used in place of the `hat' character in this revised version.) Fermionic Brownian paths are defined as paths in a space para\-metr\-ised…
The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time Markov processes. This connection allows for the creation of numerical schemes for…
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In…
In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter $H<1/2$. To establish such a…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
The vacuum-adapted formulation of quantum stochastic calculus is employed to perturb expectation semigroups via a Feynman-Kac formula. This gives an alternative perspective on the perturbation theory for quantum stochastic flows that has…
This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of the Feynman path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional…
In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…
We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the…
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…
We define a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion via an $S$-transform approach. We investigate the properties of this stochastic integral, prove the Ito formula for functions of…
This paper establishes a Feynman-Kac formula to represent the solution to general time inhomogeneous stochastic parabolic partial differential equations driven by multiplicative fractional Gaussian noises in bounded domain where L_t is a…
We consider the quantum mechanics of a charged particle in the presence of Dirac's magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum…
We prove an It\^o-Wentzell formula for the fractional Brownian motion. As an application we derive an existence and uniqueness result for a class of stochastic differential equations driven by this stochastic process.
We describe generalized Brownian motion related to parabolic equation systems from a logical point of view, i.e., as a generalization of Anderson's random walk. The connection to classical spaces is based on the Loeb measure. It seems that…
Only the "anti-Ito" integral yields the correct shift of the mean, by the fact that the elements of its Riemannian sum hold in the order O(dt) rather than only in O(sqrt dt). The corresponding "full" Fokker-Planck equation is particularly…