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Showing 1 to 11 of 11 for “"stochastic differential equation (SDE)"”.
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Complexity Analysis of Quantizations of Multidimensional Stochastic Differential Equations
… located in the field of quantizations of certain stochastic processes, namely a solution X of a multidimensional stochastic differential equation (SDE). The quantization problem for X consists in approximating X by a a random element which takes only finitely many values. Our main interest lies in …
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Analysis of Exponential Filter Time Series Operators of Geometric Brownian Motion in Trading Strategies
… where asset price dynamics are driven by a stochastic differential equation (SDE) in a continuous-time setting under the assumption of a frictionless market. A number of properties about the structure of the stochastic processes which result from the application of an exponential time series …
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Mixed Monte Carlo in the foreign exchange market
The stochastic differential equation (SDE) describing the spot FX rate is of central importance to modelling FX derivatives. A Monte Carlo estimate of the discounted individual payoffs of FX derivatives is taken to arrive at the price, provided there does not exist a closed form solution for the …
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Molecular Modeling Studies of Dendrimers and Hyperbranched Polymers
… in the entangled state. The Fokker-Planck equation from the general bead-rod-spring phase space formalism of Bird and co-workers is converted to a Stochastic Differential Equation (SDE) utilizing Ito calculus, which is then forward integrated. Two different bead-rod-spring models are …
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Conformation and Rheology of Semiflexible Macromolecules Using Non-Equilibrium Brownian Dynamics and Monte Carlo Simulations
… potential is also present. The Fokker-Planck equation describing this chain is converted to a Stochastic Differential Equation (SDE) from which the simulation algorithm for the NEBD is obtained. In steady, potential flows, the solution of the Fokker-Planck equation exists and is used in the …
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Optimizing Decision-Making under Uncertainty -- A Data-Driven Perspective
… Uncertainty Quantification for DNNs. We propose SDE-Net, an efficient method for uncertainty quantification in DNNs through the lens of dynamical systems. The central idea is to interpret DNN transformations as the state progression of a Stochastic Differential Equation (SDE), incorporating a …
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A framework for ship stability in a seastate using the state-space Fokker-Planck method
… compelling is when they interact with severe stochastic waves, resulting in a loss of stability and adversely affecting their operation. This can result in extreme motions, at the very least making life difficult for crew, to potentially the most catastrophic events capsize, and loss of cargo …
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Stochastic modelling of nutrient and predator-prey populations
This thesis first constructs a stochastic differential equation (SDE) model of a fjord nutrient, based on the hydrographic and chemical data collected from the 1991 field campaign implemented in Loch Linnhe. Stochastic modelling approach is able to account for the process noise in the nutrient …
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The Fokker-Planck and Related Equations in Theoretical Population Dynamics
… growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population …
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Random perturbations of delay differential equations at the verge of instability and periodically driven nonlinear oscillators
… the effect of small noise perturbations on delay differential equations (DDE) whose fixed point is on the verge of instability. With appropriate scaling of coordinates, the dynamics close to the fixed point can be cast in the form of a linear DDE perturbed by small noise and small nonlinearities. …
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Combinatorics of a family of stochastic differential equations with an eye towards topological temperature
… a classification of a class of scale-separated stochastic differential equations is achieved using combinatorics and formal language theory. This is extended to a topological notion of temperature and qualitative results regarding the relatedness of scale separated stochastic dynamical systems …