This thesis addresses the problem of describing the time evolution of a genetic chemical system using a stochastic approach: the Master equation approach, which is the consequence of the fundamental hypothesis of the stochastic formulation of chemical kinetics. The Master equation can be used to compute the time dependent probability distribution of the state of a chemical system. The Master eq...

A new derivation of quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with Bose field via quadratic i...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

A derivation of stochastic Schrödinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system’s quantum state given the observations made. This estimate satisfies a stoch...

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions are identified in the de-terministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in ...

It is well accepted by physicists that the Manakov PMD equation is a good model to describe the evolution of nonlinear electric elds in optical bers with randomly varying birefringence. In the regime of the di usion approximation theory, an e ective asymptotic dynamics has recently been obtained to describe this evolution. This equation is called the stochastic Manakov equation. In this article...

This paper studies first a result of existence and uniqueness of the solution to a backward stochastic differential equation driven by an infinite dimensional martingale. Then, we apply this result to find a unique solution to a backward stochastic partial differential equation in infinite dimensions. The filtration considered is an arbitrary rightcontinuous filtration, not necessarily the natu...

The problem of controlling quantum stochastic evolutions arises naturally in several different fields such as quantum chemistry, quantum information theory, quantum engineering, etc. In this paper, we apply the recently discovered closed form of the unitarity conditions for stochastic evolutions driven by the square of white noise [9] to solve this problem in the case of quadratic cost function...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

We report the first observation of stochastic resonance in confined exciton polaritons. We evidence this phenomena by tracking the polaritons behavior through two stochastic resonance quantifiers namely the spectral magnification factor and the signal-to-noise ratio. The evolution of the stochastic resonance in the function of the modulation amplitude of the periodic excitation signal is studie...