Law equivalence of stochastic linear systems

✍ Scribed by Beniamin Gołdys; Szymon Peszat

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 117 KB
• Volume: 43
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00266-1

✦ Synopsis

Let (Y ) and ( Ỹ ) be the laws on C([0; T ]; R d ) of the Gaussian processes

where K and K are entire matrix valued mappings, and W is a Wiener process. We give a necessary and su cient condition for the mutual absolute continuity of (Y ) and ( Ỹ ). As a special case we study the problem of the mutual absolute continuity of laws of partially observed Ornstein-Uhlenbeck processes.