A random Trotter product formula
Author:
Thomas G. Kurtz
Journal:
Proc. Amer. Math. Soc. 35 (1972), 147-154
MSC:
Primary 47D05; Secondary 60J35
DOI:
https://doi.org/10.1090/S0002-9939-1972-0303347-5
MathSciNet review:
0303347
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a pure jump process with state space S and let
be the succession of states visited by
the sojourn times in each state,
the number of transitions before t and
. For each
let
be an operator semigroup on a Banach space L. Define
. Conditions are given under which
will converge almost surely (or in probability) to a semigroup of operators as
. With
and


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- [2] R. Hersh and M. Pinsky, Random evolutions are asymptotically Gaussian, Comm. Pure. Appl. Math. 25 (1972), 33-44. MR 0295138 (45:4206)
- [3] Thomas G. Kurtz, A general theorem on the convergence of operator semigroups, Trans. Amer. Math. Soc. 148 (1970), 23-32. MR 41 #867. MR 0256210 (41:867)
- [4] H. F. Trotter, On the product of semi-groups of operators, Proc. Amer. Math. Soc. 10 (1959), 545-551. MR 21 #7446. MR 0108732 (21:7446)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0303347-5
Keywords:
Operator semigroup,
random evolution,
Markov process,
Trotter product
Article copyright:
© Copyright 1972
American Mathematical Society