Given a Heath–Jarrow–Morton (HJM) interest rate model M and a parametrized family of finite dimensional forward rate curves G, this paper provides a technique for projecting the infinite dimensional forward rate curve rt given by M onto the finite dimensional manifold G. The Stratonovich dynamics of the projected finite dimensional forward curve are derived and it is shown that, under the regul...

Formulae connecting the multiple Stratonovich integrals with single Ogawa and Stratonovich integrals are derived. Multiple Riemann-Stieltjes integrals with respect to certain smooth approximations of the Wiener process are considered and it is shown that these integrals converge to multiple Stratonovich integrals as the approximation converges to the Wiener process.

It is shown that a digital simulation of a noise induced phase transition using an algorithm consistent with the Ito stochastic calculus is in agreement with the predictions of that theory, whereas experiments with an analogue simulator yield measured results in agreement with the predictions of the Stratonovich theory.

Let u(t; x); t 2 R; be an adapted process parametrized by a variable x in some metric space X, (!; dx) a probability kernel on the product of the probability space and the Borel sets of X. We deal with the question whether the Stratonovich integral of u(:; x) with respect to a Wiener process on and the integral of u(t; :) with respect to the random measure (:; dx) can be interchanged. This ques...

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only ...

The Itô–Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with finite/ zero autocorrelation of the stochastic noise. The former (non-zero) noise autocorrelation structure preserves the normal chain rule using a mid-point selecti...

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of th...

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the correspondi...

Some results concerning the stability of stochastic linear partial differential equations in the sense of Stratonovich are proved. The main result ensures that a deterministic linear PDE can be stabilised by adding a suitable Stratonovich noise provided that the linear partial differential operator has negative trace.

We simulate Grover's algorithm in a classical computer by means of a stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the fixed points of the associated system of Langevin differential equations. The equations are obtained automatically for any number of qubits by employing a com...