Evolution equations have proven to be useful in tracking fine to coarse features in a single level curve and/or in an image. In this paper, we give a stochastic insight to a specific evolution equation, namely the geometric heat equation, and subsequently use this insight to develop a class of featuredriven diffusions. A progressive smoothing along desired features of a level curve is aimed at ...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

This thesis is focused around weak convergence analysis of approximations of stochastic evolution equations in Hilbert space. This is a class of problems, which is sufficiently challenging to motivate new theoretical developments in stochastic analysis. The first paper of the thesis further develops a known approach to weak convergence based on techniques from the Markov theory for the stochast...

The evolution of dispersed short-fatigue-cracks is analysed based on the equilibrium of crack-number-density (CND). By separating the mean value and the stochastic ̄uctuation of local CND, the equilibrium equation of overall CND is derived. Comparing with the mean-®eld equilibrium equation, the equilibrium equation of overall CND has di€erent forms in the expression of crack-nucleation-rate or ...

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operato...

We consider a physical model of ultrafast evolution of an initial electron distribution in a quantum wire. The electron evolution is described by a quantum-kinetic equation accounting for the interaction with phonons. A Monte Carlo approach has been developed for solving the equation. The corresponding Monte Carlo algorithm is NP -hard problem concerning the evolution time. To obtain solutions ...

We consider the simple hypothesis of letting quantum systems have an inherent random nature. Using well-known stochastic methods we thus derive a stochastic evolution operator which let us define a stochastic density operator whose expectation value under certain conditions satisfies a Lindblad equation. As natural consequences of the former assumption decoherence and spontaneous emission proce...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

We provide an approximation scheme for the maximal expected utility and optimal investment policies for the portfolio choice problem in an incomplete market. Incompleteness stems from the presence of a stochastic factor which affects the dynamics of the correlated stock price. The scheme is built on the Trotter-Kato approximation and is based on an intuitively pleasing splitting of the Hamilton...

A minimum principle for stochastic control problems with output feedback is derived by applying Bismut’s minimum principle for stochastic control problems with full information about the past to the Kushner-Stratonovitch equation describing the controlled evolution of the conditional density of the state. The well-known solution of the linear-quadratic Gaussian problem is obtained from the prin...