[PDF] Top 20 On the Effects of Different Interpretations of Stochastic Differential Equations

... a = b = c = ; the strength of the white noise σ varies. When the excitation is external, this dynamical system has a bimodal PDF. The behaviour is different with the parametric excitation of Equation (27), as one ... See full document

... impulsive differential equations, please refer to Lakshmikantham et ...non-smooth effects of the ...impulsive differential systems are very important and many results have been obtained in ... See full document

... Impulsive effects exist widely in many evolution processes in which states are changed abruptly at certain moments of time, involving such fields as biology, medicine, economics, mechanics, electronics, ... See full document

... 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 ... See full document

... To prove our main result, which is a stochastic version of the well-known LaSalle theorem (see [8,13]) for locating limit sets of Eq. (1), we will need the following nonnega- tive semi-martingale convergence ... See full document

... other types of transforms to study similar equations. Indeed the transfor- mation introduced by Zvonkin in [27], when the drift is a function, is also stated in the multidimensional case. In a series of papers the ... See full document

... One can then discuss comprehensively the existence and uniqueness as well as the structure of solutions to the initial value problem for equation (1.1) by appealing the above argument with suitable choice of γ. Here we ... See full document

... in stochastic filtering, (Dan and et al 2013) gives a formal meaning to the mixed SDE by using a flow decompo- sition which separates the stochastic integration from the deterministic rough path ... See full document

... Although Wiener introduced path integrals to study stochastic processes, these methods are not commonly used nor familiar to much of the neuroscience or applied mathematics community. There are many textbooks on ... See full document

... For stochastic differential equations, the answer to the analogous question is given by Feller’s test for explosions; see [9, Chapter ...for stochastic partial differential ... See full document

... functions of time t or constants. In the next section we give the Monte Carlo simulation, the method we will use for our experiments. In Section 3 we denote the numerical meth- ods for SDE. First, we represent a ... See full document

... There are different numerical methods for solving these kinds of differential equations (see, for example, [1], [6], [8]). Numerical methods for SDEs are recursive methods where trajectories, in ... See full document

... Solutions of nonlinear stochastic differential equations in series form.. can be put into convenient symmetrized forms which are easily calculable..[r] ... See full document

... 4. Rodkina, A: Solubility of stochastic differential equations with perturbed argument. Ukr. Math. J. 37(1), 98-103 (1985) 5. Veretennikov, AY: On strong solutions of stochastic differential ... See full document

... BOUNDARY VALUE PROBLEHS FOR STOCHASTIC DIFFERENTIAL EQUATIONS Thesis by Thomas 1 Tilliam HacDm rell In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institu[.] ... See full document

... rough stochastic PDEs and investigate convergence properties of the approximate ...one-dimensional stochastic PDEs of Burgers type driven by an additive space-time white ...these equations converge ... See full document

... Stochastic di ff erential equations (SDEs) are an essential tool to describe the randomness of a dynamic system. For example, physicists use this tool to model the time evolution of particles due to thermal ... See full document

... Our contribution is the development of a novel class of bridge constructs that are computationally and statistically efficient, simple to implement, and can be applied in scenarios where only partial and noisy ... See full document

... a differential equations model for some physical phenomenon is formulated preferably the exact solution can be ...ordinary differential equations, this is generally not possible ... See full document

... delay differential equation is a stochastic generalization of DDEs, which is systematically treated in Mohammed ...on stochastic Taylor ...as stochastic Runge–Kutta (SRK) to facilitate the ... See full document