In both classical and quantum mechanics, a dynamical system with symmetry is reduced to a system which has a smaller number of degrees of freedom. In this paper we formulate path integrals for the quantum system reduced by symmetry. The original system is defined in terms of a Riemannian manifold M , on which a Lie group G acts by isometric transformations. Then we show that the path integral o...

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium t...

We describe a path integral approach for data assimilation. It is based on the generalized hybrid Monte Carlo sampling scheme. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model in...

The paper will review the art, craft and science of modelling cavitation bubbles near boundaries through the use of the boundary integral method. The presentation will come in four parts, namely, a discussion of recent experimental studies that have motivated our current research, understanding the physics associated with the phenomena, a detailed presentation on the boundary integral method an...

The spherical functions of the noncompact Grassmann manifolds Gp,q(F) = G/K over the (skew-)fields F = R,C,H with rank q ≥ 1 and dimension parameter p > q can be described as Heckman-Opdam hypergeometric functions of type BC, where the double coset space G//K is identified with the Weyl chamber C q ⊂ R q of type B. The corresponding product formulas and Harish-Chandra integral representations w...

are suitable functions. We establish sufficient conditions for the boundedness and the convergence of x i as i → ∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.

We consider reaction-diffusion systems that can be out of equilibrium. In the preceding article a path integral formation of the Hamilton–Jacobi approximation of the Master equation of such systems. Using this path integral formulation, it is possible to calculate rate constants for the transition from one well to another well of the information potential and to give estimates of mean exit time...