Linear Stochastic Differential Equations
Efficient Techniques for Simulation of Interest Rate Models Involving Non-Linear Stochastic Differential Equations
... Efficient Techniques for Simulation of Interest Rate Models involving Non-Linear Stochastic Differential Equations 1. Introduction Driven by the increasing sophistication and competitiveness ...
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Finite difference schemes for linear stochastic integro-differential equations
... Abstract We study the rate of convergence of an explicit and an implicit-explicit finite dif- ference scheme for linear stochastic integro-differential equations of parabolic type arising in ...
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Stability of numerical method for semi linear stochastic pantograph differential equations
... of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and ...semi-linear ...
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Stability of Exponential Euler Method for Linear Stochastic Delay Differential Equations
... Keywords: Stochastic delay differential equation, Exponential euler method, Lipschitz condition, Itˆo formula, Strong ...to linear stochastic delay differential equations ...
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Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations
... mean-field stochastic differential equation, linear-quadratic optimal control, Riccati differential equation, feedback representation AMS subject classifications.. In the above, X·, valued [r] ...
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Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines
... A stochastic partial differential equation, or SPDE, describes the dynamics of a stochastic process de fi ned on a space-time ...differential equations (ODEs) by discretizing the spatial dimension of ...
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Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions
... to connect with PDEs. On the other hand, the conditions from our method are weaker than conditions offered by the Continuation Method when σ is independent of z. Moreover, our result on infinite horizon FBSDEs gives the ...
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Convergence and stability of the exponential Euler method for semi linear stochastic delay differential equations
... 6 Conclusions In this paper, we study convergence and exponential stability in mean square of the numer- ical solution for the exponential Euler method to semi-linear stochastic delay differential ...
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Stochastic control representations for penalized backward stochastic differential equations
... Let us first recall the basic idea of Krylov’s randomized stopping. For simplicity, we only consider the linear case f s (y, z) = f s . For any fixed time t ∈ [0, T ], consider a nonnegative control process (r s ) ...
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Discontinuous Quantum Stochastic Differential Equations and The Associated Kurzweil Equations
... ordinary differential equations or Kurzweil equation in applying topological dynamics to the study of ordinary differential equations as outlined in [1-3] is a major motivation for studying ...
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Mild solutions for semi-linear fractional order functional stochastic differential equations with impulse effect
... Abstract This paper is concerned with the existence results of mild solution for an impulsive fractional order stochastic differential equation with infinite delay subject to nonlocal conditions. The ...
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Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes
... determined by a quasi-linear partial differential equation of parabolic type. Recently, Bouchard and Touzi [4] propose a Monte-Carlo approach which may be more suitable for high-dimensional problems. Again ...
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Stability of stochastic differential equations in infinite dimensions
... The fundamental theory of stability was established by A. M. Lyapunov who published what is now widely known as the Lyapunov’s direct method for stability analysis in his celebrated memoir ‘The general problem of ...
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Stochastic differential equations in a scale of Hilbert spaces
... non-equilibrium stochastic dynamics of infinite particle sys- tems of the aforementioned type has been a long-standing problem, even in the case of linear drift and a single-particle diffusion ...
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Recursive Bayesian inference on stochastic differential equations
... Itô stochastic differential equations (SDE) driven by Brownian motions and the measurements are modeled as non-linear functions of the state, which are corrupted by Gaussian measurement ...
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Stability of the Stochastic Differential Equations
... of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its ...concrete stochastic dynamical systems, conditions of existence the ...
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Differential Equations and Linear Superposition
... So the equation above becomes: which is separable. Note that after the integration, we must replace u by ab+by+c to get the final solution. • In general, a appropriate substitution is a very powerful tech- nique to ...
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LINEAR DIFFERENTIAL EQUATIONS IN DISTRIBUTIONS
... a linear combination of solutions of the homogeneous equation L[r]=0, while the remainder of T corresponds to the "particular integral" of differential equations in ...
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15.2. First-Order Linear Differential Equations. First-Order Linear Differential Equations Bernoulli Equations Applications
... N is constant. Solve this differential equation to find P as a function of time if at time the size of the population is 34. Investment Growth A large corporation starts at time to continuously invest part of its ...
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Stochastic Taylor Methods for Stochastic Delay Differential Equations
... via stochastic delay differential equations ...from stochastic Taylor expansions with time delay showed a strong order of convergence of ...double stochastic integral involving time ...
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