A family of integral representations for the brownian variables
A Fixed Point Theorem In Menger Spaces
A free stochastic partial differential equation
We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra embeddable. This includes an -tuple of -Gaussian random variables e.g. for .
A general analytical result for non-linear SPDE's and applications.
A general stochastic maximum principle for singular control problems.
A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors.
A general version of the fundamental theorem of asset pricing.
A generalization of the conservation integral
Starting from the scheme given by Hudson and Parthasarathy [7,11] we extend the conservation integral to the case where the underlying operator does not commute with the time observable. It turns out that there exist two extensions, a left and a right conservation integral. Moreover, Itô's formula demands for a third integral with two integrators. Only the left integral shows similar continuity properties to that derived in [11] used for extending the integral to more than simple integrands. In...
A generalization of the Itô formula.
A generalized Itô's formula in two-dimensions and stochastic Lebesgue-Stieltjes integrals.
A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
A generalized mean-reverting equation and applications
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the...
A growth estimate for continuous random fields
We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation.
A Haussmann-Clark-Ocone formula for functionals of diffusion processes with Lipschitz coefficients.
A Hölder inequality for holomorphic functions.
A horizontal Lévy process on the bundle of orthonormal frames over a complete riemannian manifold
A hull and white formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility.
A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients.
A logarithmic Sobolev form of the Li-Yau parabolic inequality.
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities...
A lower bound for the principal eigenvalue of the Stokes operator in a random domain
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...