Wiener processes II

Lévy processes, the Wiener-Hopf factorisation and applications: part II

Cylindrical Wiener processes

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward extension of the real-valued situation. We apply this definition to introduce a stochastic integral with respect to cylindrical Wiener processes. Again, this defin...

Rotations and Tangent Processes on Wiener Space

The paper considers (a) Representations of measure preserving transformations (“rotations”) on Wiener space, and (b) The stochastic calculus of variations induced by parameterized rotations {Tθw, 0 ≤ θ ≤ ε}: “Directional derivatives” (dF (Tθw)/dθ)θ=0, “vector fields” or “tangent processes” (dTθw/dθ)θ=0 and flows of rotations.

On Wiener-Hopf factors for stable processes

We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].

First Passage Problems for Asymmetric Wiener Processes

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T .