Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type

Details Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type

2005-03-08

arxiv.org/abs/math/0503165v1

Mathematics

Probability

Scientific paper

We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and uniqueness of solutions to the martingale problem for this operator under appropriate conditions on the $a_{ij}, b_i$, and $\lam_i$. The process corresponding to $\sL$ solves an infinite dimensional stochastic differential equation similar to that for the infinite dimensional Ornstein-Uhlenbeck process.

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