- Date: 2 Jun. (Thu.)
- Place: W.W. 6th-floor, Colloquium Room & On the Web
- Time: 16:30-18:00
- Speaker: Kiyoiki Hoshino (Osaka Metropolitan University)
- Title: Extraction of random functions from the stochastic Fourier coefficients by the process with quadratic variation
- Abstract:
Let V_t be a real stochastic process with quadratic variation. Our concern is whether and how a noncausal type stochastic differential dX_t:=a(t) dV_t+b(t) dt is determined from its stochastic Fourier coefficients (SFCs for short) with respect to a CONS B of L^2[0,L]. In this talk, we use the notion of stochastic derivative to show the following: (i) when B is the Haar system, any stochastic differential dX is determined from its SFCs, (ii) when B is composed of functions of bounded variation, dX is determined from its SFCs under a certain continuity, where dX is defined by an arbitrary stochastic integral which is the inverse of the stochastic derivative.
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