EAN: 9783642882661

STOCHASTIC DIFFERENTIAL EQUATIONS - IOSIF I GIH...

Stochastic differential equations whose solutions are diffusion (or other random) processes
have been the subject of lively mathematical research since the pioneering work of Gihman  Ito
and others in the early fifties. As it gradually became clear that a great number of real
phenomena in control theory  physics  biology  economics and other areas could be modelled by
differential equations with stochastic perturbation terms  this research became somewhat
feverish  with the results that a) the number of theroretical papers alone now numbers several
hundred and b) workers interested in the field (especially from an applied viewpoint) have had
no opportunity to consult a systematic account. This monograph  written by two of the world's
authorities on prob ability theory and stochastic processes  fills this hiatus by offering the
first extensive account of the calculus of random differential equations de fined in terms of
the Wiener process. In addition to systematically ab stracting most of the salient results
obtained thus far in the theory  it includes much new material on asymptotic and stability
properties along with a potentially important generalization to equations defined with the aid
of the so-called random Poisson measure whose solutions possess jump discontinuities. Although
this monograph treats one of the most modern branches of applied mathematics  it can be read
with profit by anyone with a knowledge of elementary differential equations armed with a solid
course in stochastic processes from the measure-theoretic point of view.

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