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

**[1]**R. Hersh and R. J. Griego,*Random evolutions, Markov chains, and systems of partial differential equations*, Proc. Nat. Acad. Sci. U.S.A.**62**(1969), 305-308. MR**42**#5099. MR**0270207 (42:5099)****[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