ISSN:
1572-9036
Keywords:
stochastic partial differential equations
;
nonlinear filtering
;
random fields
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A differential calculus for random fields is developed and combined with the S-transform to obtain an explicit strong solution of the Cauchy problem $${\text{d}}u(t,x) = (Lu + cu)(t,x){\text{ d}}t + \sum\limits_{i = 1}^m {h_i u(t,x){\text{ d}}Y_t^i },$$ $$u(0,x) = u_0 (x),{\text{ }}x \in \mathbb{R}^d .$$ Here L is a linear second order elliptic operator, hi and c are real functions, and $$Y_t^i = \int_0^t {\psi ^i (s){\text{ ds}} + W_t^i } $$ , where W t is a Brownian motion. An application of the solution to nonlinear filtering and mathematical finance is also considered.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005945915199
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