We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jum...

In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F1...

We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a ver...

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process ...

For a one-parameter process of the form X, = X0 + & (b, d W, + & & ds, where W is a Wiener process and I+ d W is a stochastic integral, a twice continuously differentiable function f(X,) is again expressible as the sum of a stochastic integral and an ordinary integral via the Ito differentiation formula. In this paper we present a generalization for the stochastic integrals associated with a tw...

Four methods for the simulation of the Wiener process with constant drift and variance are described. These four methods are (1) approximating the diffusion process by a random walk with very small time steps; (2) drawing directly from the joint density of responses and reaction time by means of a (possibly) repeated application of a rejection algorithm; (3) using a discrete approximation to th...

Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices...

We consider a process (X (α) t )t∈[0,T ) given by the SDE dX (α) t = αb(t)X (α) t dt+σ(t) dBt, t ∈ [0, T ), with initial condition X 0 = 0, where T ∈ (0,∞], α ∈ R, (Bt)t∈[0,T ) is a standard Wiener process, b : [0, T ) → R \ {0} and σ : [0, T ) → (0,∞) are continuously differentiable functions. Assuming d dt ( b(t) σ(t)2 ) = −2K b(t) 2 σ(t)2 , t ∈ [0, T ), with some K ∈ R, we derive an explicit...

The Doss-Sussmann (DS) approach is used for uniform simulation of the CoxIngersoll-Ross (CIR) process. The DS formalism allows to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval...

1 The Wiener Process The stochastic process W t is a Wiener Process if its increments are normally distributed: W t − W s ∼ N (0, t − s) (1) and are independent if non-overlapping: E{(W t 1 − W s 1)(W t 2 − W s 2)} = 0 if (s 1 , t 1) ∩ (s 2 , t 2) = ∅ (2) In particular, we have E{W t − W s } = 0 (3) E{(W t − W s) 2 } = t − s (4) Furthermore, if we fix the initial value of the process to be zero...