科研之友
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摘要
Assume that X, Y are continuous-path martingales taking values in R-nu, nu %26gt;= 1, such that Y is differentially subordinate to X. The paper contains the proof of the maximal inequality %26lt;br%26gt;parallel to sup(t %26gt;= 0) vertical bar Y-t vertical bar parallel to(1) %26lt;= 2 parallel to sup(t %26gt;= 0) vertical bar X-t vertical bar parallel to(1). %26lt;br%26gt;The constant 2 is shown to be the best possible, even in the one-dimensional setting of stochastic integrals with respect to a standard Brownian motion. The proof uses Burkholder%26apos;s method and rests on the construction of an appropriate special function.
- 出版日期2013-12
