Masao Nagasawa

Markov process with creation and annihilation

SummaryA simple way is given to construct probabilistically a strong Markov process (yi, Px, η ζ of an extended sense such that the expectation u = Ex[f(yt)] provides the solution of (1.1) for a Borel measurable function c (i.e. with both terms of creation and annihilation of mass), where η and ζ stand for the dates of birth and death of a particle, respectively. Actually the (non-probability) measure Px is given as the sum of induced measures of probability measure (of Brownian motion with age) by a set of mappings. The probability measure is obtained by making killed processes of Brownian motion and piecing them together in a specific way.