Search results for "Quantum stochastic calculus"

showing 10 items of 10 documents

The Master Equation

2009

Continuous-time stochastic processsymbols.namesakeStochastic differential equationQuantum stochastic calculusStochastic processMaster equationKinetic schemesymbolsStatistical physicsChapman–Kolmogorov equationMathematics
researchProduct

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

2004

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown …

Kushner equationDifferential equationApplied MathematicsMechanical EngineeringNonlinear transformationMathematical analysisFirst-order partial differential equationFokker-Planck equationAerospace EngineeringOcean EngineeringPoisson inputItô's calculuIntegrating factorStochastic partial differential equationStochastic differential equationQuantum stochastic calculusControl and Systems EngineeringApplied mathematicsFokker–Planck equationStochastic differential calculusElectrical and Electronic EngineeringMathematicsNonlinear Dynamics
researchProduct

Non-Markovian Wave Function Simulations of Quantum Brownian Motion

2005

The non-Markovian wave function method (NMWF) using the stochastic unravelling of the master equation in the doubled Hilbert space is implemented for quantum Brownian motion. A comparison between the simulation and the analytical results shows that the method can be conveniently used to study the non-Markovian dynamics of the system.

PhysicsGeometric Brownian motiondynamicLindblad equationCondensed Matter PhysicsStochastic differential equationClassical mechanicsDiffusion processQuantum stochastic calculusQuantum stateMaster equationQuantum dissipationsystem-environment correlationsenvironment
researchProduct

The Langevin Equation

2009

PhysicsLangevin equationStochastic differential equationGeometric Brownian motionClassical mechanicsQuantum stochastic calculusDiffusion processBrownian dynamicsFokker–Planck equationBrownian motion
researchProduct

Stochastic Kinetics with Wave Nature

2003

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

PhysicsStochastic partial differential equationContinuous-time stochastic processStochastic differential equationQuantum stochastic calculusStochastic modellingDifferential equationFirst-order partial differential equationStatistical and Nonlinear PhysicsStatistical physicsPhysics::Classical PhysicsCondensed Matter PhysicsHyperbolic partial differential equationModern Physics Letters B
researchProduct

A new stochastic representation for the decay from a metastable state

2002

Abstract We show that a stochastic process on a complex plane can simulate decay from a metastable state. The simplest application of the method to a model in which the approach to equilibrium occurs through transitions over a potential barrier is discussed. The results are compared with direct numerical simulations of the stochastic differential equations describing system's evolution. We have found that the new method is much more efficient from computational point of view than the direct simulations.

Statistics and ProbabilityStochastic partial differential equationGeometric Brownian motionStochastic differential equationContinuous-time stochastic processQuantum stochastic calculusStochastic processLocal timeDiscrete-time stochastic processStatistical physicsCondensed Matter PhysicsMathematicsPhysica A: Statistical Mechanics and its Applications
researchProduct

What is Differential Stochastic Calculus?

1999

Some well known concepts of stochastic differential calculus of non linear systems corrupted by parametric normal white noise are here outlined. Ito and Stratonovich integrals concepts as well as Ito differential rule are discussed. Applications to the statistics of the response of some linear and non linear systems is also presented.

Stochastic differential equationMathematics::ProbabilityQuantum stochastic calculusMultivariable calculusStochastic calculusApplied mathematicsDifferential calculusTime-scale calculusMalliavin calculusDifferential (mathematics)Mathematics
researchProduct

Stochastic Differential Calculus

1993

In many cases of engineering interest it has become quite common to use stochastic processes to model loadings resulting from earthquake, turbulent winds or ocean waves. In these circumstances the structural response needs to be adequately described in a probabilistic sense, by evaluating the cumulants or the moments of any order of the response (see e.g. [1, 2]). In particular, for linear systems excited by normal input, the response process is normal too and the moments or the cumulants up to the second order fully characterize the probability density function of both input and output processes. Many practical problems involve processes which are approximately normal and the effect of the…

Stochastic differential equationQuantum stochastic calculusStochastic processComputer scienceLinear systemStochastic calculusTime-scale calculusStatistical physicsMalliavin calculusCumulant
researchProduct

Experimental Studies of Noise—Induced Phenomena in a Tunnel Diode

2007

Noise induced phenomena are investigated in a physical system based on a tunnel diode. The stochastic differential equation describing this physical system is analog to the Langevin equation of an overdamped Brownian particle diffusing in a nonlinear potential. This simple and versatile physical system allows a series of experiments testing and clarifying the role of the noise and of its correlation in the stochastic dynamics of bistable or metastable systems. Experimental investigations of stochastic resonance, resonant activation and noise enhanced stability are discussed.

Stochastic partial differential equationLangevin equationPhysicsStochastic differential equationQuantum stochastic calculusDifferential equationStochastic resonanceFokker–Planck equationStatistical physicsNoise (electronics)
researchProduct

Set-valued stochastic integral equations driven by martingales

2012

Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.

Stratonovich integralContinuous-time stochastic processApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISStochastic calculusRiemann–Stieltjes integralRiemann integralsymbols.namesakeQuantum stochastic calculusImproper integralsymbolsDaniell integralAnalysisMathematicsJournal of Mathematical Analysis and Applications
researchProduct