We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone r...

We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...

The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x r + and x r are evaluated. The Fresnel cosine integral C(x) is defined by C(x) = 2 π x 0 cos ...

M. Rahman t9'21 and J. R. Barber 2°'21 (1958) for a line load moving steadily over the surface of the half-plane. Both these results can be used as Green's functions to generate convolution integrals for more general boundary value problems and the availability of an explicit factorization of the rationalized form (3) of R ( V ) permits such integrals to be broken down into simpler terms by par...

We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Run...

We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum stochastic product integrals, namely a necessary and su¢ cient condition for their unitarity, and the coboundary relatio...