Related papers: Complex paths for real stochastic processes

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…

To define oscillatory movements of securities market, we put in the non-local extension of Ito- equation for wavelet-images of random processes. It is proposed an algorithm of creation of evolutionary equation and a model of prediction of…

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…

In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in…

In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…

We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogenious systems. Using the relationship between rate constants and path space partition functions, we illustrate that the…

The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during the tracking even though both start and end points are…

We employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary…

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…

In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…

In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…

Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in…

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…

The decomposition kinetics of a solid-solution into separate phases are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. This equation and the steepest-entropy-ascent quantum…

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give…

We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…

The decay rate of a metastable vacuum is usually calculated using a semiclassical approximation to the Euclidean path integral. The extension to a complete Euclidean lattice Monte Carlo computation, however, is hampered by analytic…

By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…