On Diffusion Semigroups Generated by Semi-Elliptic Differential Operators in Infinite Dimensions

  • Gottlieb Leha


We want to study some continuity properties of operator semigroups, generated by a semi-elliptic differential operator on a real separable Hilbert space ℍ. To this end, let us begin by writing the finite-dimensional semi-elliptic differential operator
$$\text{Lu(x) = }\frac{\text{1}}{\text{2}}\sum\limits_{i,j = 1}^n {a_{ij} } (x)\frac{{\partial ^2 u}}{{\partial x_i \partial x_j }}(x) + \sum\limits_{i = 1}^n {b_i } (x)\frac{{\partial u}}{{\partial x_i }}(x)$$
on ℍ = ℝn in coordinate-free form as
$$ Lu(x) = \frac{1}{2} tr u''(x)(a(x)\cdot ,\cdot ) + u'(x)(b(x))$$


Invariant Measure Stochastic Differential Equation Uniform Convergence Continuity Property Infinitesimal Generator 
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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Gottlieb Leha
    • 1
  1. 1.University of PassauPassauGermany

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