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

Gottlieb Leha
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Gottlieb Leha: University of Passau

A chapter in Potential Theory, 1988, pp 201-208 from Springer

Abstract: Abstract 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 (1) $$\text{Lu(x) = }\frac{\text{1}}{\text{2}}\sum\limits_{i,j = 1}^n {a_{ij} } (x)\frac{{\partial ^2 u}}{{\partial x_i \partial x_j }}(x) + \sum\limits_{i = 1}^n {b_i } (x)\frac{{\partial u}}{{\partial x_i }}(x)$$ on ℍ = ℝn in coordinate-free form as (1a) $$ Lu(x) = \frac{1}{2} tr u''(x)(a(x)\cdot ,\cdot ) + u'(x)(b(x))$$

Keywords: Invariant Measure; Stochastic Differential Equation; Uniform Convergence; Continuity Property; Infinitesimal Generator (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0981-9_26

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DOI: 10.1007/978-1-4613-0981-9_26

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