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Showing 1 to 20 of 63 for “"Stochastic differential equation"”.
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A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation
The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical …
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Markovian and stochastic differential equation based approaches to computer virus propagation dynamics and some models for survival distributions
… In Part I, homogeneous and non-homogeneous stochastic susceptible-exposed-infectious- recovered (SEIR) models are specifically explored for the propagation of computer virus over the Internet by borrowing ideas from mathematical epidemiology. Large computer networks such as the Internet have …
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The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation
… Lie point transformations of evolution-type equations from the contact transformation approach. We indicate that the Lie point transformations of the Fokker-Planck equation (FPE), which is a second-order linear parabolic partial differential equation (PDE), are projectable by using the …
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Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways
… shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when …
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STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION AND THEIR GENERALIZATIONS
We consider a stochastic functional differential equation with infinite memory driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We prove an existence and uniqueness result of the solution to the stochastic differential equation. We investigate the dependence of the solution on …
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Development and Application of Stochastic Methods for Radiation Belt Simulations
… which solves the radiation belt Fokker-Planck equation using its equivalent stochastic differential equations, and presents applications of this method to investigating drift shell splitting effects on radiation belt electron phase space density. The theory of the stochastic differential …
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Backward stochastic differential equations with jumps are stable
A backward stochastic differential equation is a stochastic differential equation whose terminal value is known, in contrast to a (forward) stochastic differential equation whose initial value is known, and whose solution has to be adapted to a given filtration. The main aim of this thesis is to …
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Fluid-structure interaction in noisy nonlinear systems
… this work is concerned with the application of stochastic dimensional reduction to a twelve-dimensional aeroelastic model (i.e., two degrees of freedom that characterize the aerodynamics, two auxiliary degrees of freedom, and a four dimensional real noise process). The entire analysis is done in …
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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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Simulation studies of a fluid queuing system
… the optimal control policy using simulation. Stochastic differential equations play an important role in the problem formulation and simulation. We prove that strict mathematical expression of optimal control is hard to come up with when the controller is part of the stochastic differential …
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Two Approaches to Non-Zero-Sum Stochastic Differential Games of Control and Stopping
… takes two approaches - martingale and backward stochastic differential equation (BSDE) - to solve non-zero-sum stochastic differential games in which all players can control and stop the reward streams of the games. Existence of equilibrium stopping rules is proved under some assumptions. The …
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Merton Investment Problem for the Hawkes-based Risk Model
… use the dynamic programming method to derive the stochastic Hamilton-Jacobi-Bellman (SHJB) equation satisfied by the value function. The stochastic HJB equation yields a means to obtain the optimal control and thus the optimally controlled stochastic differential equation. Finally, using the claim …
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Stochastic dynamics with singular lower order terms in finite and infinite dimensions
In this work, we aim to study several stochastic dynamics with singular coefficients. The results consist of three parts. In the first part, we study a class of second order parabolic equations $$nabla (a(t,x) cdot nabla u(t,x))+b(t,x)cdot nabla u(t,x)+V(t,x) u(t,x)-partial_{t}u(t,x)=0 eqno (1)$$ …
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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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A pure-jump market-making model for high-frequency trading
… get rid of excessive inventory. Because of the stochastic intensities of the cross-exciting point processes, the optimality condition cannot be formulated using classical Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI), so we extend the framework of constrained forward backward …
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The application of GPU to molecular communication studies
… a massive number of messenger molecule paths for stochastic evaluation. These molecules are influenced by a Brownian motion as well as the flow of the blood, which is modeled using numerical methods based on the Fokker-Planck stochastic differential equation. By using a GPU these paths can be …
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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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Hamilton-Jacobi-Bellman equation for stochastic optimal control: Applications to spacecraft attitude control
… presence of thrust uncertainty, which leads to stochastic accelerations. Spacecraft equipped with electric propulsion and other low thrust mechanisms, often experience random fluctuations in thrust. These stochastic processes arise from sources such as uncertain power supply output, varying …
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Approximation and System Identification Techniques for Stochastic Biomolecular Systems
… counts of the species are small, the inherent stochasticity in the occurrence of the reactions plays an important role in the behavior of the system. This stochasticity presents opportunities for system identification, since when a large population of cells is measured, one has many samples …
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