UW Probability Seminar
Next Seminar:
Note the unusual day, time and location.
Friday March 9, 1:30 p.m.
THO 135
Speaker: Jason Swanson (UCF)
Title: The calculus of differentials for the weak Stratonovich integral
Abstract: The weak Stratonovich integral is defined as the limit, in law, of
Stratonovich-type symmetric Riemann sums. We derive an explicit expression
for the weak Stratonovich integral of f(B) with respect to g(B), where
B is a fractional Brownian motion with Hurst parameter 1/6, and f and
g are smooth functions. We use this expression to derive an Ito-type
formula for this integral. As in the case where g is the identity, the
Ito-type formula has a correction term which is a classical Ito
integral, and which is related to the so-called signed cubic variation of
g(B). Finally, we derive a surprising formula for calculating with
differentials. We show that if dM=X dN, then Z dM can be
written as ZX dN minus a stochastic correction term which is again
related to the signed cubic variation.
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