The Symbol of a Markov Semimartingale

Name: The Symbol of a Markov Semimartingale
Brand: Shaker Verlag
Availability: OutOfStock
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By Schnurr, Jan Alexander

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Description

For L?vy processes it is a well known fact that there is a one-to-one correspondence between the elements of this class of processes and the so called continuous negative definite functions in the sense of Schoenberg ? : R d -? C. The connection between these concepts is given byE x e i(Xt-x)' ? = e -t?(?) .
In particular it is known that to every continuous negative definite function ? there exists a corresponding L?vy process (Xt)t=0. Several properties of the process can be expressed in terms of analytic properties of its characteristic exponent ?. Within the class of (universal) Markov processes, L?vy processes are those which are stochastically continuous and homogeneous in time and space. From the perspective of stochastic modeling the last point is a rather strong restriction since it means that the process 'behaves the same' on every point in space and time. Therefore, it is an interesting question if there exists a function, which is somehow similar to the characteristic exponent of a L?vy process, for a larger class of Markov processes. A class to start with is the one of (nice) Feller processes, i.e. Feller processes with the property that the test functions C8 c (Rd) are contained in the domain of their generator. In the investigation of these processes, a family of continuous negative definite functions ? ?-? p(x, ?), (x ? Rd ) shows up in the Fourier representation of the generator ? Au(x) = - e ix' ? 8 p(x, ?)?(?) d? for u ? Cc (R d ).

Product details

Binding:: Paperback
Edition:: 1
Number of Pages:: 120
Release Date:: 2009-06-04
Publication Date:: 2009-06-04
Publisher:: Shaker Verlag
Languages:: Original: English
ISBN10:: 3832282440
ISBN13:: 9783832282448
Weight:: 172 g
Height:: 149 cm
Width:: 211 cm
Thickness:: 12 cm

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