Related papers: A Feynman-Kac result via Markov BSDEs with general…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is…
In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's…
Feynman integrals are solutions to linear partial differential equations with polynomial coefficients. Using a triangle integral with general exponents as a case in point, we compare $D$-module methods to dedicated methods developed for…
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. (The theory is constructive in that, operators acting at different times, actually commute.) We first develop an operator version of the…
In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by…
This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based…
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…
In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
We consider a classical finite horizon optimal control problem for continuous-time pure jump Markov processes described by means of a rate transition measure depending on a control parameter and controlled by a feedback law. For this class…
In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on generalized k-fractional integral inequalities by considering the extended Chebyshev functional in…
We introduce a stochastic process and functional that should describe the semigroup generated by the stochastic Bessel operator. Recently Gorin and Shkolnikov showed that the largest eigenvalues for certain random matrix ensembles with soft…
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…
A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering…
Probabilistic solutions of the so called Schr\"{o}dinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for the…
We describe a solving semi-decision method based on examination of the rational structures of the generalized integrating factors of first-order ODEs. We propose a conjecture that for some family of equations of the type…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
We show that the calculation of Berezin integrals over anticommuting variables can be reduced to the evaluation of expectations of functionals of Poisson processes via an appropriate Feynman-Kac formula. In this way the tools of ordinary…
First, we consider generalized wave and scattering operators and derive modifications of commutation relations (between scattering operators and unperturbed operators) when the corresponding deviation factors behave as $\exp\{i t {\mathcal…