We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the formdXt=b(Xt)dt+σ(Xt)∘dWt,X0=x0∈Rd,t⩾0, a possibly singular drift b∈Lp(Rd), p>d and p⩾2, show that such SDEs can be approximated by random ordinary smoothing at same time. further prove support theorem for this class in rather simple way using Girsanov theorem.

The framework of the perturbed static path approximation is used to calculate the partition function of a finite Fermi system from a Hamiltonian with a separable two body interaction. Therein, the collective degree of freedom is introduced in self-consistent fashion through a Hubbard-Stratonovich transformation. In this way, all transport coefficients that dominate the decay of a metastable sys...

We exploit the separation of the …ltering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton...

These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. Next we describe the HudsonParthasarathy quantum Itô calculus and it...

In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a unifying approach for the construction of ...