A Proof of Girsanov’s Theorem: The Henstock–Kurzweil Approach

2017 ◽  
Vol 42 (2) ◽  
pp. 781-792
Author(s):  
Varayu Boonpogkrong
Keyword(s):  
Girsanov’S Theorem

Girsanov’s theorem in vector lattices

Positivity ◽  
2019 ◽  
Vol 23 (5) ◽  
pp. 1065-1099 ◽  
Author(s):  
Jacobus J. Grobler ◽  
Coenraad C. A. Labuschagne
Keyword(s):  
Vector Lattices ◽  
Girsanov’S Theorem

An extension of the mixed Novikov–Kazamaki condition

2017 ◽  
Vol 20 (04) ◽  
pp. 1750022
Author(s):  
B. Chikvinidze
Keyword(s):  
Local Martingale ◽  
Change Of Measure ◽  
Girsanov’S Theorem ◽  
Exponential Formula

Given a continuous local martingale [Formula: see text], the associated stochastic exponential [Formula: see text] is a local martingale, but not necessarily a true martingale. To know whether [Formula: see text] is a true martingale is important for many applications, e.g., if Girsanov’s theorem is applied to perform a change of measure. We give several generalizations of Kazamaki’s results and finally construct a counterexample which does not satisfy the mixed Novikov–Kazamaki condition, but satisfies our conditions.

DRIFT TRANSFORMATIONS OF SYMMETRIC DIFFUSIONS, AND DUALITY

2007 ◽  
Vol 10 (04) ◽  
pp. 613-631 ◽  
Author(s):  
P. J. FITZSIMMONS
Keyword(s):  
Diffusion Process ◽  
Dirichlet Form ◽  
Infinitesimal Generator ◽  
Probabilistic Approach ◽  
Additive Functionals ◽  
Excessive Measure ◽  
Girsanov’S Theorem ◽  
Markov Diffusion ◽  
Symmetry Measure

Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2 (m) infinitesimal generator A) and a suitable core [Formula: see text] for the Dirichlet form of X, we describe a class of derivations defined on [Formula: see text]. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence" of B is positive, then m is an excessive measure for XB, and the L2 (m) infinitesimal generator of XB is an extension of f ↦ Af + B (f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence. These methods yield a probabilistic approach to the adjoint of the semigroup of XB, and in particular lead to a solution of a problem of W. Stannat.

scholarly journals A few comments on a result of A. Novikov and Girsanov's theorem

Stochastics ◽  
2019 ◽  
Vol 91 (8) ◽  
pp. 1186-1189
Author(s):  
N. V. Krylov
Keyword(s):  
Girsanov’S Theorem

scholarly journals A non-nonstandard proof of Reimers' existence result for heat SPDEs

1998 ◽  
Vol 11 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Hassan Allouba
Keyword(s):  
Diffusion Coefficient ◽  
White Noise ◽  
Growth Condition ◽  
Existence Result ◽  
Linear Growth ◽  
Martingale Problem ◽  
Existence Of A Solution ◽  
Separate Paper ◽  
Girsanov’S Theorem ◽  
Linear Growth Condition

In 1989, Reimers gave a nonstandard proof of the existence of a solution to heat SPDEs, driven by space-time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non-nonstandard proof of this fact, and with the aid of Girsanov's theorem for continuous orthogonal martingale measures (proved in a separate paper by the author), the result is extended to the case of a measurable drift.

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