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1.
Consider a multidimensional stochastic differential equation of the form Xt=x+ò0tb(Xs-) ds+ò0tf(Xs-) dZsX_{t}=x+\int_{0}^{t}b(X_{s-})\,ds+\int_{0}^{t}f(X_{s-})\,dZ_{s}, where (Z
s
)
s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation
admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an
error expansion with respect to the time step for the difference of these densities. 相似文献
2.
In this paper, we consider the following nonlinear fractional three-point boundary-value problem:
*20c D0 + a u(t) + f( t,u(t) ) = 0, 0 < t < 1, u(0) = u¢(0) = 0, u¢(1) = ò0h u(s)\textds, \begin{array}{*{20}{c}} {D_{0 + }^\alpha u(t) + f\left( {t,u(t)} \right) = 0,\,\,\,\,0 < t < 1,} \\ {u(0) = u'(0) = 0,\,\,\,\,u'(1) = \int\limits_0^\eta {u(s){\text{d}}s,} } \\ \end{array} 相似文献
3.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}
4.
Let X={X(t),t∈ℝ
N
} be a Gaussian random field with values in ℝ
d
defined by
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